Is this grammatically correct? "There were times when you feel you don't belong."?

It is not clear just what meaning you are trying to convey. We often say "you" when we mean "a person", but we have no clear construction for doing that. It is a big plus to reqwwrite the sentence to avoid saying such clumsy things. You might say "There were times when a person would feel he didn't belong," remembering to let the tenses agree, "were" and "would feel". Whatever way you choose to say it, keep the verbs in agreement.