diff --git a/planner/core/integration_test.go b/planner/core/integration_test.go
index a8db9802903cd..0256ec56eea41 100644
--- a/planner/core/integration_test.go
+++ b/planner/core/integration_test.go
@@ -4087,3 +4087,39 @@ func (s *testIntegrationSuite) TestIssues27130(c *C) {
 		"  └─IndexRangeScan 10.00 cop[tikv] table:t3, index:a(a, b, c) range:[1,1], keep order:false, stats:pseudo",
 	))
 }
+
+func (s *testIntegrationSuite) TestIssues29711(c *C) {
+	tk := testkit.NewTestKit(c, s.store)
+	tk.MustExec("use test")
+
+	tk.MustExec("drop table if exists tbl_29711")
+	tk.MustExec("CREATE TABLE `tbl_29711` (" +
+		"`col_250` text COLLATE utf8_unicode_ci NOT NULL," +
+		"`col_251` enum('Alice','Bob','Charlie','David') COLLATE utf8_unicode_ci NOT NULL DEFAULT 'Charlie'," +
+		"PRIMARY KEY (`col_251`,`col_250`(1)) NONCLUSTERED);")
+	tk.MustQuery("explain " +
+		"select col_250,col_251 from tbl_29711 where col_251 between 'Bob' and 'David' order by col_250,col_251 limit 6;").
+		Check(testkit.Rows(
+			"TopN_9 6.00 root  test.tbl_29711.col_250, test.tbl_29711.col_251, offset:0, count:6",
+			"└─IndexLookUp_22 6.00 root  ",
+			"  ├─IndexRangeScan_19(Build) 30.00 cop[tikv] table:tbl_29711, index:PRIMARY(col_251, col_250) range:[\"Bob\",\"Bob\"], [\"Charlie\",\"Charlie\"], [\"David\",\"David\"], keep order:false, stats:pseudo",
+			"  └─TopN_21(Probe) 6.00 cop[tikv]  test.tbl_29711.col_250, test.tbl_29711.col_251, offset:0, count:6",
+			"    └─TableRowIDScan_20 30.00 cop[tikv] table:tbl_29711 keep order:false, stats:pseudo",
+		))
+
+	tk.MustExec("drop table if exists t29711")
+	tk.MustExec("CREATE TABLE `t29711` (" +
+		"`a` varchar(10) DEFAULT NULL," +
+		"`b` int(11) DEFAULT NULL," +
+		"`c` int(11) DEFAULT NULL," +
+		"KEY `ia` (`a`(2)))")
+	tk.MustQuery("explain select * from t29711 use index (ia) order by a limit 10;").
+		Check(testkit.Rows(
+			"TopN_8 10.00 root  test.t29711.a, offset:0, count:10",
+			"└─IndexLookUp_17 10.00 root  ",
+			"  ├─IndexFullScan_14(Build) 10000.00 cop[tikv] table:t29711, index:ia(a) keep order:false, stats:pseudo",
+			"  └─TopN_16(Probe) 10.00 cop[tikv]  test.t29711.a, offset:0, count:10",
+			"    └─TableRowIDScan_15 10000.00 cop[tikv] table:t29711 keep order:false, stats:pseudo",
+		))
+
+}
diff --git a/planner/core/task.go b/planner/core/task.go
index cc3486c160c77..882c0a588b276 100644
--- a/planner/core/task.go
+++ b/planner/core/task.go
@@ -1215,14 +1215,6 @@ func (p *PhysicalTopN) canPushDown(storeTp kv.StoreType) bool {
 	return expression.CanExprsPushDown(p.ctx.GetSessionVars().StmtCtx, exprs, p.ctx.GetClient(), storeTp)
 }
 
-func (p *PhysicalTopN) allColsFromSchema(schema *expression.Schema) bool {
-	cols := make([]*expression.Column, 0, len(p.ByItems))
-	for _, item := range p.ByItems {
-		cols = append(cols, expression.ExtractColumns(item.Expr)...)
-	}
-	return len(schema.ColumnsIndices(cols)) > 0
-}
-
 // GetCost computes the cost of in memory sort.
 func (p *PhysicalSort) GetCost(count float64, schema *expression.Schema) float64 {
 	if count < 2.0 {
@@ -1280,14 +1272,36 @@ func (p *PhysicalTopN) getPushedDownTopN(childPlan PhysicalPlan) *PhysicalTopN {
 	return topN
 }
 
+// canPushToIndexPlan checks if this TopN can be pushed to the index side of copTask.
+// It can be pushed to the index side when all columns used by ByItems are available from the index side and
+//   there's no prefix index column.
+func (p *PhysicalTopN) canPushToIndexPlan(indexPlan PhysicalPlan, byItemCols []*expression.Column) bool {
+	schema := indexPlan.Schema()
+	for _, col := range byItemCols {
+		pos := schema.ColumnIndex(col)
+		if pos == -1 {
+			return false
+		}
+		if schema.Columns[pos].IsPrefix {
+			return false
+		}
+	}
+	return true
+}
+
 func (p *PhysicalTopN) attach2Task(tasks ...task) task {
 	t := tasks[0].copy()
 	inputCount := t.count()
-	if copTask, ok := t.(*copTask); ok && p.canPushDown(copTask.getStoreType()) && len(copTask.rootTaskConds) == 0 {
+	cols := make([]*expression.Column, 0, len(p.ByItems))
+	for _, item := range p.ByItems {
+		cols = append(cols, expression.ExtractColumns(item.Expr)...)
+	}
+	needPushDown := len(cols) > 0
+	if copTask, ok := t.(*copTask); ok && needPushDown && p.canPushDown(copTask.getStoreType()) && len(copTask.rootTaskConds) == 0 {
 		// If all columns in topN are from index plan, we push it to index plan, otherwise we finish the index plan and
 		// push it to table plan.
 		var pushedDownTopN *PhysicalTopN
-		if !copTask.indexPlanFinished && p.allColsFromSchema(copTask.indexPlan.Schema()) {
+		if !copTask.indexPlanFinished && p.canPushToIndexPlan(copTask.indexPlan, cols) {
 			pushedDownTopN = p.getPushedDownTopN(copTask.indexPlan)
 			copTask.indexPlan = pushedDownTopN
 		} else {
@@ -1296,7 +1310,7 @@ func (p *PhysicalTopN) attach2Task(tasks ...task) task {
 			copTask.tablePlan = pushedDownTopN
 		}
 		copTask.addCost(pushedDownTopN.GetCost(inputCount, false))
-	} else if mppTask, ok := t.(*mppTask); ok && p.canPushDown(kv.TiFlash) {
+	} else if mppTask, ok := t.(*mppTask); ok && needPushDown && p.canPushDown(kv.TiFlash) {
 		pushedDownTopN := p.getPushedDownTopN(mppTask.p)
 		mppTask.p = pushedDownTopN
 	}