How do you convince your parents to let you go out with older girls?

So I met this girl that I really like, I mean she’s different than all the other girls I been with and I really find her an amazing person. I am 16 and she is 20. It sounds a little weird and crazy but you can’t always choose who you fall for. How do I explain to my mom that it is ok that I hang out with this person? Like to the point where she knows that I will be alright with this person.