Introducing priorities on rules in rewriting increases their expressive power and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe in this paper an inductive proof method for termination of priority rewriting, relying on an explicit induction on the termination property. It works by generating proof trees, modeling the rewriting relation by using abstraction and narrowing. As it specifically handles priorities on the rules, our technique allows proving termination of term rewrite systems that would diverge without priorities.