"He does not depend on his parents."
Translation:Il ne dépend pas de ses parents.
"Dependre de" is a verb + preposition combination which means "to depend on". Conjugate correctly for "depend de". Sur on its own isn't used with the indirect object (I think) but can be used with other verbs such as "concentrer sur" that also uses an indirect object. In this case "dependre de" is most appropriate.