This paper deals with problems of safe and efficient navigation algorithm for autonomous mobile robots in unknown environments. Since the obstacle avoidance algorithms are very important in mobile robot navigation, two obstacle avoidance algorithms: VFH(vector field histogram) algorithm and a fuzzy algorithm are combined to have optimal performance in various environments. And a upper-level supervisor is to select the proper one from VFH algorithm and the fuzzy algorithm according to the situations the robot faces. Computer simulation results show the effectiveness of the proposed navigation algorithm for autonomous mobile robots.