This is PHP solution, but you have to use mysqli because mysql deprecated, please read  more about mysqli.
Also, you must consider SQL injection
function save($gmt, $name, $address, $phone, $remark)
{
  if(empty($phone)){
   $phone = 'NULL';
  }else{
   $phone = "'".$phone."'";
  }
  if(empty($remark)){
   $remark = 'NULL';
  }else{
   $remark = "'".$remark."'";
  }
    $query= "INSERT INTO `user` (`gmt`, `name`, `address`, `phone`, `remark`) VALUES ('$gmt', '$name', '$address', $phone, $remark)";
    mysql_query($query);
}
//tests
save("a", "b", "c", "", "")."<br>";
save("a", "b", "c", "d", "")."<br>";
save("a", "b", "c", "d", "e")."<br>";
/*
INSERT INTO `user` (`gmt`, `name`, `address`, `phone`, `remark`) VALUES ('a', 'b', 'c', NULL, NULL)
INSERT INTO `user` (`gmt`, `name`, `address`, `phone`, `remark`) VALUES ('a', 'b', 'c', 'd', NULL)
INSERT INTO `user` (`gmt`, `name`, `address`, `phone`, `remark`) VALUES ('a', 'b', 'c', 'd', 'e')
*/
?>
DEMO