Both are not correct. your friend is wrong and you are right. I'm 20 years old. It is not correct to say "I've 20 years old." It is totally wrong.... Dont learn English from this friend :P haha.... It's a terrible mistake

To make your friend feel better, You may let him know that it is ok (but not ever done) to say: I have been alive 20 years. Along with the way you wanted to say it, You may even make it more simple.... "I'm 20." If people are already discussing age, or you are asked your age, that is all that is needed.

When I'm working with Mexican students here in California, we do a lot of work with the verbs "to be" (estar, ser) and "to have" (tener, haber). Often in Spanish you use the verb "to have" where in English we would use "to be." For example, English speakers would say: I'm 20 years old. I'm cold. I'm hungry. I'm thirsty. I'm scared. Your classmate directly translated the Spanish and hasn't learned these differences yet.

You're correct I'm/I am 20 years old.

I am 20 years old. Sure