diff --git a/pkg/planner/core/integration_test.go b/pkg/planner/core/integration_test.go
index 453a9b4c0dabc..d3228d8060f08 100644
--- a/pkg/planner/core/integration_test.go
+++ b/pkg/planner/core/integration_test.go
@@ -1075,6 +1075,31 @@ func TestTiFlashFineGrainedShuffleWithMaxTiFlashThreads(t *testing.T) {
 	require.Equal(t, uint64(16), streamCount[0])
 }
 
+func TestIssue37986(t *testing.T) {
+	store := testkit.CreateMockStore(t)
+	tk := testkit.NewTestKit(t, store)
+	tk.MustExec("use test")
+
+	tk.MustExec(`drop table if exists t3`)
+	tk.MustExec(`CREATE TABLE t3(c0 INT, primary key(c0))`)
+	tk.MustExec(`insert into t3 values(1), (2), (3), (4), (5), (6), (7), (8), (9), (10)`)
+	rs := tk.MustQuery(`SELECT v2.c0 FROM (select rand() as c0 from t3) v2 order by v2.c0 limit 10`).Rows()
+	lastVal := -1.0
+	for _, r := range rs {
+		v := r[0].(string)
+		val, err := strconv.ParseFloat(v, 64)
+		require.NoError(t, err)
+		require.True(t, val >= lastVal)
+		lastVal = val
+	}
+
+	tk.MustQuery(`explain format='brief' SELECT v2.c0 FROM (select rand() as c0 from t3) v2 order by v2.c0 limit 10`).
+		Check(testkit.Rows(`TopN 10.00 root  Column#2, offset:0, count:10`,
+			`└─Projection 10000.00 root  rand()->Column#2`,
+			`  └─TableReader 10000.00 root  data:TableFullScan`,
+			`    └─TableFullScan 10000.00 cop[tikv] table:t3 keep order:false, stats:pseudo`))
+}
+
 func TestIssue33175(t *testing.T) {
 	store := testkit.CreateMockStore(t)
 	tk := testkit.NewTestKit(t, store)
diff --git a/pkg/planner/core/rule_topn_push_down.go b/pkg/planner/core/rule_topn_push_down.go
index 830995f55387d..5f4d73b0c3e8c 100644
--- a/pkg/planner/core/rule_topn_push_down.go
+++ b/pkg/planner/core/rule_topn_push_down.go
@@ -134,8 +134,17 @@ func (p *LogicalProjection) pushDownTopN(topN *LogicalTopN, opt *util.LogicalOpt
 	}
 	if topN != nil {
 		exprCtx := p.SCtx().GetExprCtx()
+		substitutedExprs := make([]expression.Expression, 0, len(topN.ByItems))
 		for _, by := range topN.ByItems {
-			by.Expr = expression.FoldConstant(exprCtx, expression.ColumnSubstitute(exprCtx, by.Expr, p.schema, p.Exprs))
+			substituted := expression.FoldConstant(exprCtx, expression.ColumnSubstitute(exprCtx, by.Expr, p.schema, p.Exprs))
+			if !expression.IsImmutableFunc(substituted) {
+				// after substituting, if the order-by expression is un-deterministic like 'order by rand()', stop pushing down.
+				return p.baseLogicalPlan.pushDownTopN(topN, opt)
+			}
+			substitutedExprs = append(substitutedExprs, substituted)
+		}
+		for i, by := range topN.ByItems {
+			by.Expr = substitutedExprs[i]
 		}
 
 		// remove meaningless constant sort items.