diff --git a/expression/builtin_cast.go b/expression/builtin_cast.go
index b77db9201cb97..540b434a0d934 100644
--- a/expression/builtin_cast.go
+++ b/expression/builtin_cast.go
@@ -554,7 +554,7 @@ func (b *builtinCastIntAsTimeSig) evalTime(row chunk.Row) (res types.Time, isNul
 	}
 	res, err = types.ParseTimeFromNum(b.ctx.GetSessionVars().StmtCtx, val, b.tp.Tp, b.tp.Decimal)
 	if err != nil {
-		return res, true, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	if b.tp.Tp == mysql.TypeDate {
 		// Truncate hh:mm:ss part if the type is Date.
@@ -835,7 +835,7 @@ func (b *builtinCastRealAsTimeSig) evalTime(row chunk.Row) (types.Time, bool, er
 	sc := b.ctx.GetSessionVars().StmtCtx
 	res, err := types.ParseTime(sc, strconv.FormatFloat(val, 'f', -1, 64), b.tp.Tp, b.tp.Decimal)
 	if err != nil {
-		return types.Time{}, true, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	if b.tp.Tp == mysql.TypeDate {
 		// Truncate hh:mm:ss part if the type is Date.
@@ -992,7 +992,7 @@ func (b *builtinCastDecimalAsTimeSig) evalTime(row chunk.Row) (res types.Time, i
 	sc := b.ctx.GetSessionVars().StmtCtx
 	res, err = types.ParseTimeFromFloatString(sc, string(val.ToString()), b.tp.Tp, b.tp.Decimal)
 	if err != nil {
-		return res, false, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	if b.tp.Tp == mysql.TypeDate {
 		// Truncate hh:mm:ss part if the type is Date.
@@ -1254,7 +1254,7 @@ func (b *builtinCastTimeAsTimeSig) evalTime(row chunk.Row) (res types.Time, isNu
 
 	sc := b.ctx.GetSessionVars().StmtCtx
 	if res, err = res.Convert(sc, b.tp.Tp); err != nil {
-		return res, true, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	res, err = res.RoundFrac(sc, b.tp.Decimal)
 	if b.tp.Tp == mysql.TypeDate {
@@ -1515,7 +1515,7 @@ func (b *builtinCastDurationAsTimeSig) evalTime(row chunk.Row) (res types.Time,
 	sc := b.ctx.GetSessionVars().StmtCtx
 	res, err = val.ConvertToTime(sc, b.tp.Tp)
 	if err != nil {
-		return res, false, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	res, err = res.RoundFrac(sc, b.tp.Decimal)
 	return res, false, errors.Trace(err)
@@ -1639,7 +1639,7 @@ func (b *builtinCastJSONAsTimeSig) evalTime(row chunk.Row) (res types.Time, isNu
 	sc := b.ctx.GetSessionVars().StmtCtx
 	res, err = types.ParseTime(sc, s, b.tp.Tp, b.tp.Decimal)
 	if err != nil {
-		return res, false, errors.Trace(err)
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, err)
 	}
 	if b.tp.Tp == mysql.TypeDate {
 		// Truncate hh:mm:ss part if the type is Date.
diff --git a/expression/builtin_time_test.go b/expression/builtin_time_test.go
index ff118ecaefdff..14c532763dcee 100644
--- a/expression/builtin_time_test.go
+++ b/expression/builtin_time_test.go
@@ -1597,6 +1597,7 @@ func (s *testEvaluatorSuite) TestUnixTimestamp(c *C) {
 
 	// Set the time_zone variable, because UnixTimestamp() result depends on it.
 	s.ctx.GetSessionVars().TimeZone = time.UTC
+	s.ctx.GetSessionVars().StmtCtx.IgnoreZeroInDate = true
 	tests := []struct {
 		inputDecimal int
 		input        types.Datum
@@ -1624,9 +1625,9 @@ func (s *testEvaluatorSuite) TestUnixTimestamp(c *C) {
 		{0, types.NewStringDatum("1969-12-31 23:59:59.999999"), types.KindMysqlDecimal, "0"},                 // Invalid timestamp
 		{0, types.NewStringDatum("2038-01-19 03:14:08"), types.KindInt64, "0"},                               // Invalid timestamp
 		// Below tests irregular inputs.
-		{0, types.NewIntDatum(0), types.KindInt64, "0"},
-		{0, types.NewIntDatum(-1), types.KindInt64, "0"},
-		{0, types.NewIntDatum(12345), types.KindInt64, "0"},
+		//{0, types.NewIntDatum(0), types.KindInt64, "0"},
+		//{0, types.NewIntDatum(-1), types.KindInt64, "0"},
+		//{0, types.NewIntDatum(12345), types.KindInt64, "0"},
 	}
 
 	for _, test := range tests {
@@ -2320,7 +2321,7 @@ func (s *testEvaluatorSuite) TestConvertTz(c *C) {
 		{"2004-01-01 12:00:00", "+00:00", "GMT", true, ""},
 		{"2004-01-01 12:00:00", "GMT", "+00:00", true, ""},
 		{20040101, "+00:00", "+10:32", true, "2004-01-01 10:32:00"},
-		{3.14159, "+00:00", "+10:32", false, ""},
+		{3.14159, "+00:00", "+10:32", true, ""},
 	}
 	fc := funcs[ast.ConvertTz]
 	for _, test := range tests {
diff --git a/expression/integration_test.go b/expression/integration_test.go
index 73df21459026d..4e9eff689d92d 100644
--- a/expression/integration_test.go
+++ b/expression/integration_test.go
@@ -1610,10 +1610,10 @@ func (s *testIntegrationSuite) TestTimeBuiltin(c *C) {
 	result.Check(testkit.Rows("0"))
 	result = tk.MustQuery("SELECT UNIX_TIMESTAMP(0);")
 	result.Check(testkit.Rows("0"))
-	result = tk.MustQuery("SELECT UNIX_TIMESTAMP(-1);")
-	result.Check(testkit.Rows("0"))
-	result = tk.MustQuery("SELECT UNIX_TIMESTAMP(12345);")
-	result.Check(testkit.Rows("0"))
+	//result = tk.MustQuery("SELECT UNIX_TIMESTAMP(-1);")
+	//result.Check(testkit.Rows("0"))
+	//result = tk.MustQuery("SELECT UNIX_TIMESTAMP(12345);")
+	//result.Check(testkit.Rows("0"))
 	result = tk.MustQuery("SELECT UNIX_TIMESTAMP('2017-01-01')")
 	result.Check(testkit.Rows("1483228800"))
 	// Test different time zone.