diff --git a/expression/builtin_time.go b/expression/builtin_time.go
index 7fddd000837aa..42b37ada48c38 100644
--- a/expression/builtin_time.go
+++ b/expression/builtin_time.go
@@ -5641,7 +5641,7 @@ func (b *builtinLastDaySig) evalTime(row chunk.Row) (types.Time, bool, error) {
 	tm := arg.Time
 	var day int
 	year, month := tm.Year(), tm.Month()
-	if year == 0 && month == 0 && tm.Day() == 0 {
+	if month == 0 {
 		return types.Time{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(arg.String()))
 	}
 	day = types.GetLastDay(year, month)
diff --git a/expression/builtin_time_test.go b/expression/builtin_time_test.go
index c368dbd530a06..b2669ffb5a062 100644
--- a/expression/builtin_time_test.go
+++ b/expression/builtin_time_test.go
@@ -2428,6 +2428,8 @@ func (s *testEvaluatorSuite) TestLastDay(c *C) {
 		"0000-00-00",
 		"1992-13-00",
 		"2007-10-07 23:59:61",
+		"2005-00-00",
+		"2005-00-01",
 		123456789}
 
 	for _, i := range testsNull {