diff --git a/pkg/statistics/handle/globalstats/global_stats.go b/pkg/statistics/handle/globalstats/global_stats.go
index c366b96a51c4f..4eff64fc0961b 100644
--- a/pkg/statistics/handle/globalstats/global_stats.go
+++ b/pkg/statistics/handle/globalstats/global_stats.go
@@ -305,10 +305,15 @@ func blockingMergePartitionStats2GlobalStats(
 		}
 		// FMSketch use many memory, so we first deal with it and then destroy it.
 		// Merge FMSketch.
+		// NOTE: allFms maybe contain empty.
 		globalStats.Fms[i] = allFms[i][0]
 		for j := 1; j < len(allFms[i]); j++ {
-			globalStats.Fms[i].MergeFMSketch(allFms[i][j])
-			allFms[i][j].DestroyAndPutToPool()
+			if globalStats.Fms[i] == nil {
+				globalStats.Fms[i] = allFms[i][j]
+			} else {
+				globalStats.Fms[i].MergeFMSketch(allFms[i][j])
+				allFms[i][j].DestroyAndPutToPool()
+			}
 		}
 
 		// Update the global NDV.
diff --git a/tests/realtikvtest/statisticstest/statistics_test.go b/tests/realtikvtest/statisticstest/statistics_test.go
index 6dcc5d65f5e50..5535a387e73d4 100644
--- a/tests/realtikvtest/statisticstest/statistics_test.go
+++ b/tests/realtikvtest/statisticstest/statistics_test.go
@@ -185,3 +185,50 @@ func TestNewCollationStatsWithPrefixIndex(t *testing.T) {
 		"1 3 15 0 2 0",
 	))
 }
+
+func TestBlockMergeFMSketch(t *testing.T) {
+	store := realtikvtest.CreateMockStoreAndSetup(t)
+	tk := testkit.NewTestKit(t, store)
+	tk.MustExec("use test")
+	tk.MustExec("set @@tidb_enable_async_merge_global_stats=OFF;")
+	defer func() {
+		tk.MustExec("set @@tidb_enable_async_merge_global_stats=ON;")
+	}()
+	checkFMSketch(tk)
+}
+
+func TestAsyncMergeFMSketch(t *testing.T) {
+	store := realtikvtest.CreateMockStoreAndSetup(t)
+	tk := testkit.NewTestKit(t, store)
+	tk.MustExec("use test")
+	tk.MustExec("set @@tidb_enable_async_merge_global_stats=ON;")
+	checkFMSketch(tk)
+}
+
+func checkFMSketch(tk *testkit.TestKit) {
+	tk.MustExec(`CREATE TABLE employees  (id INT NOT NULL AUTO_INCREMENT PRIMARY KEY,fname VARCHAR(25) NOT NULL,lname VARCHAR(25) NOT NULL,store_id INT NOT NULL,department_id INT NOT NULL
+) PARTITION BY RANGE(id)  (
+    PARTITION p0 VALUES LESS THAN (5),
+    PARTITION p1 VALUES LESS THAN (10),
+    PARTITION p2 VALUES LESS THAN (15),
+    PARTITION p3 VALUES LESS THAN MAXVALUE
+);`)
+	tk.MustExec(`INSERT INTO employees(FNAME,LNAME,STORE_ID,DEPARTMENT_ID) VALUES
+    ('Bob', 'Taylor', 3, 2), ('Frank', 'Williams', 1, 2),
+    ('Ellen', 'Johnson', 3, 4), ('Jim', 'Smith', 2, 4),
+    ('Mary', 'Jones', 1, 1), ('Linda', 'Black', 2, 3),
+    ('Ed', 'Jones', 2, 1), ('June', 'Wilson', 3, 1),
+    ('Andy', 'Smith', 1, 3), ('Lou', 'Waters', 2, 4),
+    ('Jill', 'Stone', 1, 4), ('Roger', 'White', 3, 2),
+    ('Howard', 'Andrews', 1, 2), ('Fred', 'Goldberg', 3, 3),
+    ('Barbara', 'Brown', 2, 3), ('Alice', 'Rogers', 2, 2),
+    ('Mark', 'Morgan', 3, 3), ('Karen', 'Cole', 3, 2);`)
+	tk.MustExec("ANALYZE TABLE employees;")
+	tk.MustExec("select * from employees;")
+	tk.MustExec("alter table employees truncate partition p0;")
+	tk.MustExec("select * from employees;")
+	tk.MustExec("analyze table employees partition p3;")
+	tk.MustExec("select * from employees;")
+	tk.MustQuery(`SHOW STATS_HISTOGRAMS WHERE TABLE_NAME='employees' and partition_name="global"  and column_name="id"`).CheckAt([]int{6}, [][]any{
+		{"14"}})
+}