diff --git a/mysql-test/r/alter_table.result b/mysql-test/r/alter_table.result
index 5df0c2e3c96..e572fdb197c 100644
--- a/mysql-test/r/alter_table.result
+++ b/mysql-test/r/alter_table.result
@@ -2012,3 +2012,12 @@ t1	CREATE TABLE `t1` (
   UNIQUE KEY `idx` (`i`)
 ) ENGINE=MyISAM DEFAULT CHARSET=latin1
 DROP TABLE t1;
+CREATE TABLE t1 (
+`event_id` bigint(20) unsigned NOT NULL DEFAULT '0',
+`market_id` bigint(20) unsigned NOT NULL DEFAULT '0',
+PRIMARY KEY (`event_id`,`market_id`)
+);
+ALTER TABLE t1 ADD PRIMARY KEY IF NOT EXISTS event_id (event_id,market_id);
+Warnings:
+Note	1061	Multiple primary key defined
+DROP TABLE t1;
diff --git a/mysql-test/t/alter_table.test b/mysql-test/t/alter_table.test
index 4dde3ed6971..05d915ec478 100644
--- a/mysql-test/t/alter_table.test
+++ b/mysql-test/t/alter_table.test
@@ -1699,3 +1699,16 @@ alter table t1 add unique index if not exists idx(i);
 alter table t1 add unique index if not exists idx(i);
 show create table t1;
 DROP TABLE t1;
+
+#
+# MDEV-8358 ADD PRIMARY KEY IF NOT EXISTS -> ERROR 1068 (42000): Multiple primary key
+#
+
+CREATE TABLE t1 (
+   `event_id` bigint(20) unsigned NOT NULL DEFAULT '0',
+   `market_id` bigint(20) unsigned NOT NULL DEFAULT '0',
+ PRIMARY KEY (`event_id`,`market_id`)
+ );
+ALTER TABLE t1 ADD PRIMARY KEY IF NOT EXISTS event_id (event_id,market_id);
+DROP TABLE t1;
+
diff --git a/sql/sql_table.cc b/sql/sql_table.cc
index 5ad4ceb9c35..e0f7184b0e8 100644
--- a/sql/sql_table.cc
+++ b/sql/sql_table.cc
@@ -5846,6 +5846,16 @@ drop_create_field:
     {
       if (!key->create_if_not_exists)
         continue;
+
+      /* Check if the table already has a PRIMARY KEY */
+      if (key->type == Key::PRIMARY &&
+          table->s->primary_key != MAX_KEY)
+      {
+        push_warning_printf(thd, Sql_condition::WARN_LEVEL_NOTE,
+            ER_DUP_KEYNAME, ER(ER_MULTIPLE_PRI_KEY));
+        goto remove_key_no_warn;
+      }
+
       /* If the name of the key is not specified,     */
       /* let us check the name of the first key part. */
       if ((keyname= key->name.str) == NULL)
@@ -5912,6 +5922,7 @@ drop_create_field:
 remove_key:
       push_warning_printf(thd, Sql_condition::WARN_LEVEL_NOTE,
           ER_DUP_KEYNAME, ER(ER_DUP_KEYNAME), keyname);
+remove_key_no_warn:
       key_it.remove();
       if (key->type == Key::FOREIGN_KEY)
       {