This paper describes a motion planning method for mobile robot which considers the path ambiguity of moving obstacles. Each moving obstacle has a set of paths and their probabilities. The robot selects the motion which minimizes the expected time to reach its goal, by recursively predicting future states of each obstacle and then selecting the best motion for them. To calculate the motion for terminal nodes of the search tree, we use a randomized motion planner, which is an improved version of a previous method. Simulation results show the effectiveness of the proposed method.