diff --git a/mysql-test/r/mysqldump.result b/mysql-test/r/mysqldump.result
index b484cf7c51d6b62271a23d0306dcea47f8ccb246..1bf8d78cd9e7087fe702d42320e0d1cf4401609c 100644
--- a/mysql-test/r/mysqldump.result
+++ b/mysql-test/r/mysqldump.result
@@ -1,3 +1,8 @@
+Bug#37938 - Test "mysqldump" lacks various insert statements
+Turn off concurrent inserts to avoid random errors
+NOTE:  We reset the variable back to saved value at the end of test
+SET @OLD_CONCURRENT_INSERT = @@GLOBAL.CONCURRENT_INSERT;
+SET @@GLOBAL.CONCURRENT_INSERT = 0;
 DROP TABLE IF EXISTS t1, `"t"1`, t1aa, t2, t2aa, t3;
 drop database if exists mysqldump_test_db;
 drop database if exists db1;
@@ -3565,6 +3570,7 @@ DROP TABLE t1,t2;
 
 
 -- Dump completed on DATE
+SET @@GLOBAL.CONCURRENT_INSERT = @OLD_CONCURRENT_INSERT;
 #
 # End of 5.0 tests
 #
diff --git a/mysql-test/t/mysqldump.test b/mysql-test/t/mysqldump.test
index 88053ae95fb86951eb7fba619977a9f8ed885d1b..2f11685385fef996b08cbb653eb0e49ae79990f9 100644
--- a/mysql-test/t/mysqldump.test
+++ b/mysql-test/t/mysqldump.test
@@ -5,6 +5,14 @@
 # Binlog is required
 --source include/have_log_bin.inc
 
+
+--echo Bug#37938 - Test "mysqldump" lacks various insert statements
+--echo Turn off concurrent inserts to avoid random errors
+--echo NOTE:  We reset the variable back to saved value at the end of test
+SET @OLD_CONCURRENT_INSERT = @@GLOBAL.CONCURRENT_INSERT;
+SET @@GLOBAL.CONCURRENT_INSERT = 0;
+
+
 --disable_warnings
 DROP TABLE IF EXISTS t1, `"t"1`, t1aa, t2, t2aa, t3;
 drop database if exists mysqldump_test_db;
@@ -1594,6 +1602,10 @@ DROP TABLE t1,t2;
 --replace_regex /-- [^D][^u][^m][^p].*// /\/\*!.*// / on [0-9 :-]+/ on DATE/
 --exec $MYSQL_DUMP test
 
+# We reset concurrent_inserts value to whatever it was at the start of the test
+SET @@GLOBAL.CONCURRENT_INSERT = @OLD_CONCURRENT_INSERT;
+
+
 --echo #
 --echo # End of 5.0 tests
 --echo #