diff --git a/pkg/session/bootstrap.go b/pkg/session/bootstrap.go
index 0a24c5cbaa266..3c96e2e82d8e7 100644
--- a/pkg/session/bootstrap.go
+++ b/pkg/session/bootstrap.go
@@ -1203,11 +1203,15 @@ const (
 	// version 239
 	// add modify_params to tidb_global_task and tidb_global_task_history.
 	version239 = 239
+
+	// version 240
+	// Add indexes to mysql.analyze_jobs to speed up the query.
+	version240 = 240
 )
 
 // currentBootstrapVersion is defined as a variable, so we can modify its value for testing.
 // please make sure this is the largest version
-var currentBootstrapVersion int64 = version239
+var currentBootstrapVersion int64 = version240
 
 // DDL owner key's expired time is ManagerSessionTTL seconds, we should wait the time and give more time to have a chance to finish it.
 var internalSQLTimeout = owner.ManagerSessionTTL + 15
@@ -1382,6 +1386,7 @@ var (
 		upgradeToVer217,
 		upgradeToVer218,
 		upgradeToVer239,
+		upgradeToVer240,
 	}
 )
 
@@ -3287,6 +3292,14 @@ func upgradeToVer239(s sessiontypes.Session, ver int64) {
 	doReentrantDDL(s, "ALTER TABLE mysql.tidb_global_task_history ADD COLUMN modify_params json AFTER `error`;", infoschema.ErrColumnExists)
 }
 
+func upgradeToVer240(s sessiontypes.Session, ver int64) {
+	if ver >= version240 {
+		return
+	}
+	doReentrantDDL(s, "ALTER TABLE mysql.analyze_jobs ADD INDEX idx_schema_table_state (table_schema, table_name, state)", dbterror.ErrDupKeyName)
+	doReentrantDDL(s, "ALTER TABLE mysql.analyze_jobs ADD INDEX idx_schema_table_partition_state (table_schema, table_name, partition_name, state)", dbterror.ErrDupKeyName)
+}
+
 // initGlobalVariableIfNotExists initialize a global variable with specific val if it does not exist.
 func initGlobalVariableIfNotExists(s sessiontypes.Session, name string, val any) {
 	ctx := kv.WithInternalSourceType(context.Background(), kv.InternalTxnBootstrap)
diff --git a/pkg/session/bootstrap_test.go b/pkg/session/bootstrap_test.go
index d4d4f75d4f882..a786ef95b3093 100644
--- a/pkg/session/bootstrap_test.go
+++ b/pkg/session/bootstrap_test.go
@@ -2524,3 +2524,48 @@ func TestIndexJoinMultiPatternByUpgrade650To840(t *testing.T) {
 	require.Equal(t, 1, row.Len())
 	require.Equal(t, int64(0), row.GetInt64(0))
 }
+
+func TestTiDBUpgradeToVer240(t *testing.T) {
+	ctx := context.Background()
+	store, dom := CreateStoreAndBootstrap(t)
+	defer func() { require.NoError(t, store.Close()) }()
+
+	ver239 := version239
+	seV239 := CreateSessionAndSetID(t, store)
+	txn, err := store.Begin()
+	require.NoError(t, err)
+	m := meta.NewMutator(txn)
+	err = m.FinishBootstrap(int64(ver239))
+	require.NoError(t, err)
+	revertVersionAndVariables(t, seV239, ver239)
+	err = txn.Commit(ctx)
+	require.NoError(t, err)
+	store.SetOption(StoreBootstrappedKey, nil)
+
+	// Check index not exist.
+	res := MustExecToRecodeSet(t, seV239, "show create table mysql.analyze_jobs")
+	chk := res.NewChunk(nil)
+	err = res.Next(ctx, chk)
+	require.NoError(t, err)
+	require.Equal(t, 1, chk.NumRows())
+	require.NotContains(t, string(chk.GetRow(0).GetBytes(1)), "idx_schema_table_state")
+	require.NotContains(t, string(chk.GetRow(0).GetBytes(1)), "idx_schema_table_partition_state")
+
+	dom.Close()
+	domCurVer, err := BootstrapSession(store)
+	require.NoError(t, err)
+	defer domCurVer.Close()
+	seCurVer := CreateSessionAndSetID(t, store)
+	ver, err := getBootstrapVersion(seCurVer)
+	require.NoError(t, err)
+	require.Equal(t, currentBootstrapVersion, ver)
+
+	// Check index exist.
+	res = MustExecToRecodeSet(t, seCurVer, "show create table mysql.analyze_jobs")
+	chk = res.NewChunk(nil)
+	err = res.Next(ctx, chk)
+	require.NoError(t, err)
+	require.Equal(t, 1, chk.NumRows())
+	require.Contains(t, string(chk.GetRow(0).GetBytes(1)), "idx_schema_table_state")
+	require.Contains(t, string(chk.GetRow(0).GetBytes(1)), "idx_schema_table_partition_state")
+}