This study presents an obstacle avoidance method for Autonomous Mobile Robot by Fuzzy Potential Method (FPM) considering velocities of obstacles relative to the robot. The FPM, which is presented by Tsuzaki, is action control method for autonomous mobile robot. In the proposed method, to decide a velocity vector command of the robot to avoid moving obstacles safely, Potential Membership Function (PMF) considering time until colliding and relative velocity is designed. By means of considering predicted positions of the robot and the obstacle calculated from the time and the relative velocity, the robot can start avoiding behaviour at an appropriate time according to the velocity of the obstacle and the robot. To verify the effectiveness of the proposed method, numerical simulations and simplified experiment intended for an omni-directional autonomous mobile robot are carried out.