diff --git a/expression/column.go b/expression/column.go
index 986ed8b7b66a7..1ea9c1a41595a 100644
--- a/expression/column.go
+++ b/expression/column.go
@@ -196,6 +196,13 @@ type Column struct {
 	OrigName string
 	IsHidden bool
 
+	// IsPrefix indicates whether this column is a prefix column in index.
+	//
+	// for example:
+	// 	pk(col1, col2), index(col1(10)), key: col1(10)_col1_col2 => index's col1 will be true
+	// 	pk(col1(10), col2), index(col1), key: col1_col1(10)_col2 => pk's col1 will be true
+	IsPrefix bool
+
 	// InOperand indicates whether this column is the inner operand of column equal condition converted
 	// from `[not] in (subq)`.
 	InOperand bool
@@ -504,6 +511,11 @@ func ColInfo2Col(cols []*Column, col *model.ColumnInfo) *Column {
 func indexCol2Col(colInfos []*model.ColumnInfo, cols []*Column, col *model.IndexColumn) *Column {
 	for i, info := range colInfos {
 		if info.Name.L == col.Name.L {
+			if col.Length > 0 && info.FieldType.Flen > col.Length {
+				c := *cols[i]
+				c.IsPrefix = true
+				return &c
+			}
 			return cols[i]
 		}
 	}
diff --git a/planner/core/integration_test.go b/planner/core/integration_test.go
index 8ef77e8eebf26..15805ff617e92 100644
--- a/planner/core/integration_test.go
+++ b/planner/core/integration_test.go
@@ -2125,3 +2125,39 @@ func (s *testIntegrationSuite) TestIssue27797(c *C) {
 	result = tk.MustQuery("select col2 from IDT_HP24172 where col1 = 8388607 and col1 in (select col1 from IDT_HP24172);")
 	result.Check(testkit.Rows("<nil>"))
 }
+
+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` varchar(10) COLLATE utf8_unicode_ci NOT NULL," +
+		"PRIMARY KEY (`col_251`,`col_250`(1)));")
+	tk.MustQuery("explain " +
+		"select /*+ LIMIT_TO_COP() */ col_250,col_251 from tbl_29711 use index (primary) 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:asc, test.tbl_29711.col_251:asc, offset:0, count:6",
+			"└─IndexLookUp_15 6.00 root  ",
+			"  ├─IndexRangeScan_12(Build) 250.00 cop[tikv] table:tbl_29711, index:PRIMARY(col_251, col_250) range:[\"Bob\",\"David\"], keep order:false, stats:pseudo",
+			"  └─TopN_14(Probe) 6.00 cop[tikv]  test.tbl_29711.col_250:asc, test.tbl_29711.col_251:asc, offset:0, count:6",
+			"    └─TableRowIDScan_13 250.00 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 /*+ LIMIT_TO_COP() */ * from t29711 use index (ia) order by a limit 10;").
+		Check(testkit.Rows(
+			"TopN_8 10.00 root  test.t29711.a:asc, offset:0, count:10",
+			"└─IndexLookUp_14 10.00 root  ",
+			"  ├─IndexFullScan_11(Build) 10000.00 cop[tikv] table:t29711, index:ia(a) keep order:false, stats:pseudo",
+			"  └─TopN_13(Probe) 10.00 cop[tikv]  test.t29711.a:asc, offset:0, count:10",
+			"    └─TableRowIDScan_12 10000.00 cop[tikv] table:t29711 keep order:false, stats:pseudo",
+		))
+
+}
diff --git a/planner/core/task.go b/planner/core/task.go
index 3789a9f00dd50..0386c253d765d 100644
--- a/planner/core/task.go
+++ b/planner/core/task.go
@@ -955,14 +955,36 @@ 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) && 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) && 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 {