diff --git a/types/time.go b/types/time.go
index d626c08018fc3..6ad62302e5e9c 100644
--- a/types/time.go
+++ b/types/time.go
@@ -443,7 +443,13 @@ func (t Time) RoundFrac(sc *stmtctx.StatementContext, fsp int) (Time, error) {
 
 // GetFsp gets the fsp of a string.
 func GetFsp(s string) (fsp int) {
-	fsp = len(s) - strings.LastIndex(s, ".") - 1
+	index := GetFracIndex(s)
+	if index < 0 {
+		fsp = 0
+	} else {
+		fsp = len(s) - index - 1
+	}
+
 	if fsp == len(s) {
 		fsp = 0
 	} else if fsp > 6 {
@@ -452,6 +458,22 @@ func GetFsp(s string) (fsp int) {
 	return
 }
 
+// GetFracIndex finds the last '.' for get fracStr, index = -1 means fracStr not found.
+// but for format like '2019.01.01 00:00:00', the index should be -1.
+func GetFracIndex(s string) (index int) {
+	index = -1
+	for i := len(s) - 1; i >= 0; i-- {
+		if unicode.IsPunct(rune(s[i])) {
+			if s[i] == '.' {
+				index = i
+			}
+			break
+		}
+	}
+
+	return index
+}
+
 // RoundFrac rounds fractional seconds precision with new fsp and returns a new one.
 // We will use the “round half up” rule, e.g, >= 0.5 -> 1, < 0.5 -> 0,
 // so 2011:11:11 10:10:10.888888 round 0 -> 2011:11:11 10:10:11
@@ -640,9 +662,10 @@ func ParseDateFormat(format string) []string {
 // See https://dev.mysql.com/doc/refman/5.7/en/date-and-time-literals.html.
 // The only delimiter recognized between a date and time part and a fractional seconds part is the decimal point.
 func splitDateTime(format string) (seps []string, fracStr string) {
-	if i := strings.LastIndex(format, "."); i > 0 {
-		fracStr = strings.TrimSpace(format[i+1:])
-		format = format[:i]
+	index := GetFracIndex(format)
+	if index > 0 {
+		fracStr = format[index+1:]
+		format = format[:index]
 	}
 
 	seps = ParseDateFormat(format)
@@ -727,6 +750,15 @@ func parseDatetime(sc *stmtctx.StatementContext, str string, fsp int, isFloat bo
 			sc.AppendWarning(ErrTruncatedWrongValue.GenWithStackByArgs("datetime", str))
 			err = nil
 		}
+	case 2:
+		// YYYY-MM is not valid
+		if len(fracStr) == 0 {
+			return ZeroDatetime, errors.Trace(ErrIncorrectDatetimeValue.GenWithStackByArgs(str))
+		}
+
+		// YYYY-MM.DD, DD is treat as fracStr
+		err = scanTimeArgs(append(seps, fracStr), &year, &month, &day)
+		fracStr = ""
 	case 3:
 		// YYYY-MM-DD
 		err = scanTimeArgs(seps, &year, &month, &day)
diff --git a/types/time_test.go b/types/time_test.go
index 65175757740f6..9021c61614a36 100644
--- a/types/time_test.go
+++ b/types/time_test.go
@@ -62,6 +62,9 @@ func (s *testTimeSuite) TestDateTime(c *C) {
 		{"170102036", "2017-01-02 03:06:00"},
 		{"170102039.", "2017-01-02 03:09:00"},
 		{"170102037.11", "2017-01-02 03:07:11.00"},
+		{"2018.01.01", "2018-01-01 00:00:00.00"},
+		{"2018/01/01-00:00:00", "2018-01-01 00:00:00"},
+		{"2018.01.01 00:00:00", "2018-01-01 00:00:00"},
 	}
 
 	for _, test := range table {
@@ -83,6 +86,9 @@ func (s *testTimeSuite) TestDateTime(c *C) {
 		{"2017-01-05 23:59:59.575601", 0, "2017-01-06 00:00:00"},
 		{"2017-01-31 23:59:59.575601", 0, "2017-02-01 00:00:00"},
 		{"2017-00-05 23:59:58.575601", 3, "2017-00-05 23:59:58.576"},
+		{"2017.00.05 23:59:58.575601", 3, "2017-00-05 23:59:58.576"},
+		{"2017/00/05 23:59:58.575601", 3, "2017-00-05 23:59:58.576"},
+		{"2017/00/05-23:59:58.575601", 3, "2017-00-05 23:59:58.576"},
 	}
 
 	for _, test := range fspTbl {
@@ -103,6 +109,8 @@ func (s *testTimeSuite) TestDateTime(c *C) {
 		"1000-09-31 00:00:00",
 		"1001-02-29 00:00:00",
 		"20170118.999",
+		"2018-01",
+		"2018.01",
 	}
 
 	for _, test := range errTable {
@@ -152,6 +160,8 @@ func (s *testTimeSuite) TestDate(c *C) {
 		{"2015-06-01 12:12:12", "2015-06-01"},
 		{"0001-01-01 00:00:00", "0001-01-01"},
 		{"0001-01-01", "0001-01-01"},
+		{"2019.01.01", "2019-01-01"},
+		{"2019/01/01", "2019-01-01"},
 	}
 
 	for _, test := range table {
@@ -162,6 +172,7 @@ func (s *testTimeSuite) TestDate(c *C) {
 
 	errTable := []string{
 		"0121231",
+		"2019.01",
 	}
 
 	for _, test := range errTable {
@@ -1307,3 +1318,18 @@ func (s *testTimeSuite) TestGetFormatType(c *C) {
 	c.Assert(isDuration, Equals, true)
 	c.Assert(isDate, Equals, false)
 }
+
+func (s *testTimeSuite) TestgetFracIndex(c *C) {
+	testCases := []struct {
+		str         string
+		expectIndex int
+	}{
+		{"2019.01.01 00:00:00", -1},
+		{"2019.01.01 00:00:00.1", 19},
+		{"12345.6", 5},
+	}
+	for _, testCase := range testCases {
+		index := types.GetFracIndex(testCase.str)
+		c.Assert(index, Equals, testCase.expectIndex)
+	}
+}