This brief investigates the robust optimal tracking control for a three Mecanum wheeled mobile robot (MWMR) with the external disturbance by the aid of online actor-critic synchronous learning algorithm. The Euler-Lagrange motion equation of MWMR subject to slipping is established by analyzing the structural characteristics of Mecanum wheels. Concatenating the tracking error with the desired trajectory, the tracking control problem is converted into a time-invariant optimal control problem of an augmented system. Then, an approximate optimal tracking controller is obtained by applying online actor-critic synchronous learning algorithm. With the help of Lyapunov-based analysis, the ultimately bounded tracking can be guaranteed. Finally, simulation results show the effectiveness of synchronous learning algorithm and approximate optimal tracking controller.