diff --git a/expression/builtin_time.go b/expression/builtin_time.go
index 98e7876321609..d3ca3138a29df 100644
--- a/expression/builtin_time.go
+++ b/expression/builtin_time.go
@@ -7037,7 +7037,7 @@ func (b *builtinLastDaySig) evalTime(row chunk.Row) (types.Time, bool, error) {
 	}
 	tm := arg
 	year, month := tm.Year(), tm.Month()
-	if arg.InvalidZero() {
+	if tm.Month() == 0 || (tm.Day() == 0 && b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode()) {
 		return types.ZeroTime, true, handleInvalidTimeError(b.ctx, types.ErrWrongValue.GenWithStackByArgs(types.DateTimeStr, arg.String()))
 	}
 	lastDay := types.GetLastDay(year, month)
diff --git a/expression/builtin_time_test.go b/expression/builtin_time_test.go
index 4015794377486..d466b0a8070ea 100644
--- a/expression/builtin_time_test.go
+++ b/expression/builtin_time_test.go
@@ -2758,22 +2758,35 @@ func (s *testEvaluatorSuite) TestLastDay(c *C) {
 		c.Assert(result, Equals, test.expect)
 	}
 
-	testsNull := []interface{}{
-		"0000-00-00",
-		"1992-13-00",
-		"2007-10-07 23:59:61",
-		"2005-00-00",
-		"2005-00-01",
-		"2243-01 00:00:00",
-		123456789}
+	var timeData types.Time
+	timeData.StrToDate(s.ctx.GetSessionVars().StmtCtx, "202010", "%Y%m")
+	testsNull := []struct {
+		param           interface{}
+		isNilNoZeroDate bool
+		isNil           bool
+	}{
+		{"0000-00-00", true, true},
+		{"1992-13-00", true, true},
+		{"2007-10-07 23:59:61", true, true},
+		{"2005-00-00", true, true},
+		{"2005-00-01", true, true},
+		{"2243-01 00:00:00", true, true},
+		{123456789, true, true},
+		{timeData, true, false},
+	}
 
 	for _, i := range testsNull {
-		t := []types.Datum{types.NewDatum(i)}
+		t := []types.Datum{types.NewDatum(i.param)}
 		f, err := fc.getFunction(s.ctx, s.datumsToConstants(t))
 		c.Assert(err, IsNil)
 		d, err := evalBuiltinFunc(f, chunk.Row{})
 		c.Assert(err, IsNil)
-		c.Assert(d.IsNull(), IsTrue)
+		c.Assert(d.IsNull() == i.isNilNoZeroDate, IsTrue)
+		s.ctx.GetSessionVars().SQLMode &= ^mysql.ModeNoZeroDate
+		d, err = evalBuiltinFunc(f, chunk.Row{})
+		c.Assert(err, IsNil)
+		c.Assert(d.IsNull() == i.isNil, IsTrue)
+		s.ctx.GetSessionVars().SQLMode |= mysql.ModeNoZeroDate
 	}
 }
 
diff --git a/expression/builtin_time_vec.go b/expression/builtin_time_vec.go
index 6f74a8f587e50..6bbad73063468 100644
--- a/expression/builtin_time_vec.go
+++ b/expression/builtin_time_vec.go
@@ -712,15 +712,15 @@ func (b *builtinLastDaySig) vecEvalTime(input *chunk.Chunk, result *chunk.Column
 		if result.IsNull(i) {
 			continue
 		}
-		if times[i].InvalidZero() {
+		tm := times[i]
+		year, month := tm.Year(), tm.Month()
+		if tm.Month() == 0 || (tm.Day() == 0 && b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode()) {
 			if err := handleInvalidTimeError(b.ctx, types.ErrWrongValue.GenWithStackByArgs(types.DateTimeStr, times[i].String())); err != nil {
 				return err
 			}
 			result.SetNull(i, true)
 			continue
 		}
-		tm := times[i]
-		year, month := tm.Year(), tm.Month()
 		lastDay := types.GetLastDay(year, month)
 		times[i] = types.NewTime(types.FromDate(year, month, lastDay, 0, 0, 0, 0), mysql.TypeDate, types.DefaultFsp)
 	}