A practical path planning method for a multiple mobile robot system (MMRS) requires handling both the collision-free constraint and the kinematic constraint of real robots, the latter of which has to date been neglected by most path planning methods. In this paper, we present a practical cooperative path planning algorithm for MMRS in a dynamic environment. First, each robot uses an analytical method to plan an obstacle-avoidance path. Then, a distributed prioritized scheme is introduced to realize cooperative path planning. In the scheme, each robot calculates a priority value according to its situation at each instant in time, which will determine the robot's priority. Higher-priority robots can ignore lower-priority robots, whereas lower-priority robots should avoid collisions with higher-priority robots. To minimize the path length for MMRS, a least path length constraint is added. The priority value is also calculated by a path cost function that takes the path length into consideration. Unlike other priority methods, the algorithm proposed is not time consuming; therefore, it is suitable for dynamic environments. Simulation results are presented to verify the effectiveness of the proposed algorithm.