After analyzing the behavior of accessed users, browsers and existing Markov prediction models, a TOP-N selective Markov model was presented to predict user next requests. The TOP-N consisted of URLs which requested time was over N in Web logs. The Markov chains were made up of user visit sessions. If the session which user visited currently matched one of the Markov chains, the next URL of this Markov chains in TOP-N would be prefetched in local cache. The experiment results show that this model can achieve dramatic improvement on predictive accuracy and get a good hit ratio with reducing the traffic load to some extent.