diff --git a/cmd/explaintest/r/select.result b/cmd/explaintest/r/select.result
index bce3ecf8ba436..573fa51565556 100644
--- a/cmd/explaintest/r/select.result
+++ b/cmd/explaintest/r/select.result
@@ -432,3 +432,36 @@ Projection_7	10000.00	root	6_aux_0
   │ └─TableScan_9	10000.00	cop	table:t1, range:[-inf,+inf], keep order:false, stats:pseudo
   └─TableReader_12	10000.00	root	data:TableScan_11
     └─TableScan_11	10000.00	cop	table:t2, range:[-inf,+inf], keep order:false, stats:pseudo
+drop table if exists t;
+create table t(a int, b int);
+explain select a from t order by rand();
+id	count	task	operator info
+Projection_8	10000.00	root	test.t.a
+└─Sort_4	10000.00	root	col_1:asc
+  └─Projection_9	10000.00	root	test.t.a, rand()
+    └─TableReader_7	10000.00	root	data:TableScan_6
+      └─TableScan_6	10000.00	cop	table:t, range:[-inf,+inf], keep order:false, stats:pseudo
+explain select a, b from t order by abs(2);
+id	count	task	operator info
+TableReader_8	10000.00	root	data:TableScan_7
+└─TableScan_7	10000.00	cop	table:t, range:[-inf,+inf], keep order:false, stats:pseudo
+explain select a from t order by abs(rand())+1;
+id	count	task	operator info
+Projection_8	10000.00	root	test.t.a
+└─Sort_4	10000.00	root	col_1:asc
+  └─Projection_9	10000.00	root	test.t.a, plus(abs(rand()), 1)
+    └─TableReader_7	10000.00	root	data:TableScan_6
+      └─TableScan_6	10000.00	cop	table:t, range:[-inf,+inf], keep order:false, stats:pseudo
+drop table if exists t1;
+create table t1(a int, b int);
+drop table if exists t2;
+create table t2(a int, b int);
+explain select * from t1 where t1.a in (select t2.a as a from t2 where t2.b > t1.b order by t1.b);
+id	count	task	operator info
+Apply_11	9990.00	root	semi join, inner:TableReader_19, equal:[eq(test.t1.a, test.t2.a)]
+├─TableReader_14	9990.00	root	data:Selection_13
+│ └─Selection_13	9990.00	cop	not(isnull(test.t1.a))
+│   └─TableScan_12	10000.00	cop	table:t1, range:[-inf,+inf], keep order:false, stats:pseudo
+└─TableReader_19	7992.00	root	data:Selection_18
+  └─Selection_18	7992.00	cop	gt(test.t2.b, test.t1.b), not(isnull(test.t2.a))
+    └─TableScan_17	10000.00	cop	table:t2, range:[-inf,+inf], keep order:false, stats:pseudo
diff --git a/cmd/explaintest/t/select.test b/cmd/explaintest/t/select.test
index a5b04f20f463b..3f3fb13d71031 100644
--- a/cmd/explaintest/t/select.test
+++ b/cmd/explaintest/t/select.test
@@ -203,3 +203,17 @@ explain select a in (select a+b from t t2 where t2.b = t1.b) from t t1;
 drop table t;
 create table t(a int not null, b int);
 explain select a in (select a from t t2 where t2.b = t1.b) from t t1;
+
+# test order by rand()
+drop table if exists t;
+create table t(a int, b int);
+explain select a from t order by rand();
+explain select a, b from t order by abs(2);
+explain select a from t order by abs(rand())+1;
+
+# test order by correlated column
+drop table if exists t1;
+create table t1(a int, b int);
+drop table if exists t2;
+create table t2(a int, b int);
+explain select * from t1 where t1.a in (select t2.a as a from t2 where t2.b > t1.b order by t1.b);
diff --git a/executor/sort_test.go b/executor/sort_test.go
deleted file mode 100644
index 3cc18f5953c8f..0000000000000
--- a/executor/sort_test.go
+++ /dev/null
@@ -1,46 +0,0 @@
-// Copyright 2019 PingCAP, Inc.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-package executor_test
-
-import (
-	. "github.com/pingcap/check"
-	"github.com/pingcap/tidb/util/testkit"
-)
-
-func (s *testSuite4) TestSortRand(c *C) {
-	tk := testkit.NewTestKit(c, s.store)
-	tk.MustExec("use test")
-	tk.MustExec("drop table if exists t")
-	tk.MustExec("create table t(a int, b int);")
-
-	tk.MustQuery("explain select a from t order by rand()").Check(testkit.Rows(
-		"Projection_8 10000.00 root test.t.a",
-		"└─Sort_4 10000.00 root col_1:asc",
-		"  └─Projection_9 10000.00 root test.t.a, rand()",
-		"    └─TableReader_7 10000.00 root data:TableScan_6",
-		"      └─TableScan_6 10000.00 cop table:t, range:[-inf,+inf], keep order:false, stats:pseudo",
-	))
-
-	tk.MustQuery("explain select a, b from t order by abs(2)").Check(testkit.Rows(
-		"TableReader_8 10000.00 root data:TableScan_7",
-		"└─TableScan_7 10000.00 cop table:t, range:[-inf,+inf], keep order:false, stats:pseudo"))
-
-	tk.MustQuery("explain select a from t order by abs(rand())+1").Check(testkit.Rows(
-		"Projection_8 10000.00 root test.t.a",
-		"└─Sort_4 10000.00 root col_1:asc",
-		"  └─Projection_9 10000.00 root test.t.a, plus(abs(rand()), 1)",
-		"    └─TableReader_7 10000.00 root data:TableScan_6",
-		"      └─TableScan_6 10000.00 cop table:t, range:[-inf,+inf], keep order:false, stats:pseudo",
-	))
-}
diff --git a/expression/column.go b/expression/column.go
index c76db51d924ed..055f22207c688 100644
--- a/expression/column.go
+++ b/expression/column.go
@@ -160,7 +160,7 @@ func (col *CorrelatedColumn) IsCorrelated() bool {
 
 // ConstItem implements Expression interface.
 func (col *CorrelatedColumn) ConstItem() bool {
-	return true
+	return false
 }
 
 // Decorrelate implements Expression interface.
diff --git a/expression/column_test.go b/expression/column_test.go
index e821ef1fd96a4..66aaec0e5f2f0 100644
--- a/expression/column_test.go
+++ b/expression/column_test.go
@@ -46,7 +46,7 @@ func (s *testEvaluatorSuite) TestColumn(c *C) {
 	c.Assert(corCol.Equal(nil, corCol), IsTrue)
 	c.Assert(corCol.Equal(nil, invalidCorCol), IsFalse)
 	c.Assert(corCol.IsCorrelated(), IsTrue)
-	c.Assert(corCol.ConstItem(), IsTrue)
+	c.Assert(corCol.ConstItem(), IsFalse)
 	c.Assert(corCol.Decorrelate(schema).Equal(nil, col), IsTrue)
 	c.Assert(invalidCorCol.Decorrelate(schema).Equal(nil, invalidCorCol), IsTrue)
 
diff --git a/expression/expression.go b/expression/expression.go
index 7ce4bd835fdd4..bbada8e5dda08 100644
--- a/expression/expression.go
+++ b/expression/expression.go
@@ -108,6 +108,7 @@ type Expression interface {
 	IsCorrelated() bool
 
 	// ConstItem checks if this expression is constant item, regardless of query evaluation state.
+	// A constant item can be eval() when build a plan.
 	// An expression is constant item if it:
 	// refers no tables.
 	// refers no subqueries that refers any tables.
diff --git a/expression/util.go b/expression/util.go
index 14a6cc94122fb..8db743abf3f30 100644
--- a/expression/util.go
+++ b/expression/util.go
@@ -632,22 +632,22 @@ func BuildNotNullExpr(ctx sessionctx.Context, expr Expression) Expression {
 	return notNull
 }
 
-// isMutableEffectsExpr checks if expr contains function which is mutable or has side effects.
-func isMutableEffectsExpr(expr Expression) bool {
+// IsMutableEffectsExpr checks if expr contains function which is mutable or has side effects.
+func IsMutableEffectsExpr(expr Expression) bool {
 	switch x := expr.(type) {
 	case *ScalarFunction:
 		if _, ok := mutableEffectsFunctions[x.FuncName.L]; ok {
 			return true
 		}
 		for _, arg := range x.GetArgs() {
-			if isMutableEffectsExpr(arg) {
+			if IsMutableEffectsExpr(arg) {
 				return true
 			}
 		}
 	case *Column:
 	case *Constant:
 		if x.DeferredExpr != nil {
-			return isMutableEffectsExpr(x.DeferredExpr)
+			return IsMutableEffectsExpr(x.DeferredExpr)
 		}
 	}
 	return false
@@ -661,7 +661,7 @@ func RemoveDupExprs(ctx sessionctx.Context, exprs []Expression) []Expression {
 	sc := ctx.GetSessionVars().StmtCtx
 	for _, expr := range exprs {
 		key := string(expr.HashCode(sc))
-		if _, ok := exists[key]; !ok || isMutableEffectsExpr(expr) {
+		if _, ok := exists[key]; !ok || IsMutableEffectsExpr(expr) {
 			res = append(res, expr)
 			exists[key] = struct{}{}
 		}
diff --git a/planner/core/rule_column_pruning.go b/planner/core/rule_column_pruning.go
index 2d8d3cfaf6073..c0b3bbda3bccd 100644
--- a/planner/core/rule_column_pruning.go
+++ b/planner/core/rule_column_pruning.go
@@ -149,12 +149,14 @@ func (la *LogicalAggregation) PruneColumns(parentUsedCols []*expression.Column)
 }
 
 // PruneColumns implements LogicalPlan interface.
+// If any expression can view as a constant in execution stage, such as correlated column, constant,
+// we do prune them. Note that we can't prune the expressions contain non-deterministic functions, such as rand().
 func (ls *LogicalSort) PruneColumns(parentUsedCols []*expression.Column) error {
 	child := ls.children[0]
 	for i := len(ls.ByItems) - 1; i >= 0; i-- {
 		cols := expression.ExtractColumns(ls.ByItems[i].Expr)
 		if len(cols) == 0 {
-			if !ls.ByItems[i].Expr.ConstItem() {
+			if expression.IsMutableEffectsExpr(ls.ByItems[i].Expr) {
 				continue
 			}
 			ls.ByItems = append(ls.ByItems[:i], ls.ByItems[i+1:]...)