All you can really do is show your parents you are responsible. They will probably allow you to date when they trust you to make good decisions. If they have an age in mind when they will let you date -- and if you haven't reached that age yet -- then maybe the best you can do for now is group activities including the guy, or have him over for dinner with your parents.
Try communicating with your parents about this... Keep in mind the WORST thing you can do is throw a temper tantrum if you don't get your way. That will prove to them that you aren't mature enough to date.