diff --git a/executor/analyze.go b/executor/analyze.go
index 4a16ba9ed07e7..821b7d0626398 100644
--- a/executor/analyze.go
+++ b/executor/analyze.go
@@ -42,6 +42,7 @@ import (
 	"github.com/pingcap/tidb/util/chunk"
 	"github.com/pingcap/tidb/util/dbterror/exeerrors"
 	"github.com/pingcap/tidb/util/logutil"
+	"github.com/pingcap/tidb/util/mathutil"
 	"github.com/pingcap/tidb/util/sqlexec"
 	"github.com/pingcap/tipb/go-tipb"
 	"go.uber.org/zap"
@@ -184,7 +185,7 @@ func (e *AnalyzeExec) Next(ctx context.Context, _ *chunk.Chunk) error {
 	// needGlobalStats used to indicate whether we should merge the partition-level stats to global-level stats.
 	needGlobalStats := pruneMode == variable.Dynamic
 	globalStatsMap := make(map[globalStatsKey]globalStatsInfo)
-	err = e.handleResultsError(ctx, concurrency, needGlobalStats, globalStatsMap, resultsCh)
+	err = e.handleResultsError(ctx, concurrency, needGlobalStats, globalStatsMap, resultsCh, len(tasks))
 	for _, task := range tasks {
 		if task.colExec != nil && task.colExec.memTracker != nil {
 			task.colExec.memTracker.Detach()
@@ -275,10 +276,18 @@ func recordHistoricalStats(sctx sessionctx.Context, tableID int64) error {
 }
 
 // handleResultsError will handle the error fetch from resultsCh and record it in log
-func (e *AnalyzeExec) handleResultsError(ctx context.Context, concurrency int, needGlobalStats bool,
-	globalStatsMap globalStatsMap, resultsCh <-chan *statistics.AnalyzeResults) error {
+func (e *AnalyzeExec) handleResultsError(
+	ctx context.Context,
+	concurrency int,
+	needGlobalStats bool,
+	globalStatsMap globalStatsMap,
+	resultsCh <-chan *statistics.AnalyzeResults,
+	taskNum int,
+) error {
 	partitionStatsConcurrency := e.ctx.GetSessionVars().AnalyzePartitionConcurrency
-	// If 'partitionStatsConcurrency' > 1, we will try to demand extra session from Domain to save Analyze results in concurrency.
+	// the concurrency of handleResultsError cannot be more than partitionStatsConcurrency
+	partitionStatsConcurrency = mathutil.Min(taskNum, partitionStatsConcurrency)
+	// If partitionStatsConcurrency > 1, we will try to demand extra session from Domain to save Analyze results in concurrency.
 	// If there is no extra session we can use, we will save analyze results in single-thread.
 	if partitionStatsConcurrency > 1 {
 		dom := domain.GetDomain(e.ctx)