The movie is about a man who is still young and he can't see his painted photo, otherwise he will be old, and in the end of the movie he will see his photo and he will die.
May be you are talking about The League of extraordinary Gentlemen having the Dorian Gray Character. A wiki link on the film is here. The character you are talking about is Dorian Gray (played by Stuart Townsend). He remains youthful by not looking into his own portrait. As a result the portrait ages instead of him and he becomes immortal. But at the end of the movie Mina confronts Dorian and kills him by exposing his portrait to him.