diff --git a/expression/builtin_time.go b/expression/builtin_time.go
index 44842541a41ff..ba08265945dc6 100644
--- a/expression/builtin_time.go
+++ b/expression/builtin_time.go
@@ -1847,6 +1847,9 @@ func (b *builtinStrToDateDateSig) evalTime(row chunk.Row) (types.Time, bool, err
 	if !succ {
 		return types.Time{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
 	}
+	if b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode() && (t.Time.Year() == 0 || t.Time.Month() == 0 || t.Time.Day() == 0) {
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
+	}
 	t.Type, t.Fsp = mysql.TypeDate, types.MinFsp
 	return t, false, nil
 }
@@ -1876,6 +1879,9 @@ func (b *builtinStrToDateDatetimeSig) evalTime(row chunk.Row) (types.Time, bool,
 	if !succ {
 		return types.Time{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
 	}
+	if b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode() && (t.Time.Year() == 0 || t.Time.Month() == 0 || t.Time.Day() == 0) {
+		return types.Time{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
+	}
 	t.Type, t.Fsp = mysql.TypeDatetime, b.tp.Decimal
 	return t, false, nil
 }
@@ -1908,6 +1914,9 @@ func (b *builtinStrToDateDurationSig) evalDuration(row chunk.Row) (types.Duratio
 	if !succ {
 		return types.Duration{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
 	}
+	if b.ctx.GetSessionVars().SQLMode.HasNoZeroDateMode() && (t.Time.Year() == 0 || t.Time.Month() == 0 || t.Time.Day() == 0) {
+		return types.Duration{}, true, handleInvalidTimeError(b.ctx, types.ErrIncorrectDatetimeValue.GenWithStackByArgs(t.String()))
+	}
 	t.Fsp = b.tp.Decimal
 	dur, err := t.ConvertToDuration()
 	return dur, err != nil, err
diff --git a/expression/integration_test.go b/expression/integration_test.go
index 73f27629ee844..6bd91b57691bf 100644
--- a/expression/integration_test.go
+++ b/expression/integration_test.go
@@ -4135,6 +4135,37 @@ func (s *testIntegrationSuite) TestDecimalConvertToTime(c *C) {
 	tk.MustQuery("select * from t").Check(testkit.Rows("2001-01-01 10:00:00.123456 2011-07-07 10:11:12"))
 }
 
+func (s *testIntegrationSuite) TestIssue9732(c *C) {
+	tk := testkit.NewTestKit(c, s.store)
+	defer s.cleanEnv(c)
+
+	tk.MustQuery(`select monthname(str_to_date(null, '%m')), monthname(str_to_date(null, '%m')),
+monthname(str_to_date(1, '%m')), monthname(str_to_date(0, '%m'));`).Check(testkit.Rows("<nil> <nil> <nil> <nil>"))
+
+	nullCases := []struct {
+		sql string
+		ret string
+	}{
+		{"select str_to_date(1, '%m')", "0000-01-00"},
+		{"select str_to_date(01, '%d')", "0000-00-01"},
+		{"select str_to_date(2019, '%Y')", "2019-00-00"},
+		{"select str_to_date('5,2019','%m,%Y')", "2019-05-00"},
+		{"select str_to_date('01,2019','%d,%Y')", "2019-00-01"},
+		{"select str_to_date('01,5','%d,%m')", "0000-05-01"},
+	}
+
+	for _, nullCase := range nullCases {
+		tk.MustQuery(nullCase.sql).Check(testkit.Rows("<nil>"))
+	}
+
+	// remove NO_ZERO_DATE mode
+	tk.MustExec("set sql_mode='ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION'")
+
+	for _, nullCase := range nullCases {
+		tk.MustQuery(nullCase.sql).Check(testkit.Rows(nullCase.ret))
+	}
+}
+
 func (s *testIntegrationSuite) TestDaynameArithmetic(c *C) {
 	tk := testkit.NewTestKit(c, s.store)
 	defer s.cleanEnv(c)