An effective method of obstacle avoidance for omni-directional mobile robots is proposed to avoid moving obstacles in dynamic environments. Our method uses the concept of circle lists which represent the trajectories of robot and obstacles. This method predicts not only collision position but also collision time, and hence it enables the robot avoiding the most urgent collision first. In order to avoid obstacles, our method uses artificial repulsive force and contraction force. Simulation results show that the robot could avoid obstacles effectively.