Introducing priorities on rules increases the expressive power of rewriting and helps to limit computations. Priority rewriting is used as a com- putation model for the functional paradigm. Termination of priority rewriting then warrants that programs give a result. We describe in this paper an induc- tive proof method for termination of priority rewriting, lying on an inductive mechanism on the termination property. It works by generating proof trees, using abstraction and narrowing. As it specifically handles priorities on the rules, our technique allows proving termination of rewrite systems that would diverge without priorities.