Is one of your friend a correct sentence?

Nope.

One of something... the something should be plural - friends.

Nope.

It lacks a subject. There is a verb/predicate - Is (Which, by the way, should not be capitalized.). There is a predicate nominative - one. There is an adjectival prepositional phrase that modifies "one" - of your friend(s). But there is no subject, e.g., a third person pronoun (he, she, it) or a proper personal name (Tom, Ed, Mary). Lacking a subject, there is no sentence.