In this paper, the design method of the Inverse Optimal Controller (IOC) is proposed for the Mecanum Wheeled Mobile Robot (MWMR) to implement the trajectory-tracking mission. First, a kinematic and dynamic model is introduced for the MWMR. And then, the inverse optimal controller is designed for the trajectory tracking problem of MWMR based on the Control Lyapunov Function (CLF) and passivity approaches to ensure the stability and robustness of the system, where the controller gains are synthesized to achieve passivity. Finally, simulations were conducted to verify the performance of the proposed control method in trajectory tracking with minor errors. The results substantiate the feasibility and efficacy of the presented method.