This paper introduces the current research status of sliding mode control (SMC) in omnidirectional mobile robot control, and gives some researches we have done recently, as well as our researches in future work. Some researches about trajectory tracking of omnidirectional mobile robots, which are driven by using SMC, are summarized. The advantages and disadvantages in previous researches are analyzed. The kinematics and dynamics of omnidirectional mobile robots with four mecanum wheels (OMRFMW) are established. Based on the kinematics and dynamics models, the control law of OMRFMW is put forward to realize trajectory tracking. Then, stability of the proposed control strategy is analyzed. Simulations of the proposed control strategy for OMRFMW are carried out. The simulation results show that the proposed strategy performs well and has good tracking performance.