In this paper, we propose a predictive system for the avoidance of the moving obstacle. In the dynamic environment, robots should travel to the target point without collision with the moving obstacle. For this, we need the prediction of the position and velocity of the moving obstacle. So, we use the Kalman filer algorithm for the prediction. And for the application of the Kalman filter algorithm about the real time travel, we obtain the position of the obstacle which has the future time using Fuzzy system. Through the computer simulation studies, we show the effectiveness of the proposed navigational algorithm for autonomous mobile robots.