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Aiming at the trajectory tracking problem under discontinuous stretch, the predictive controller based on observation is designed. Firstly, the kinematics model of the mobile robot is established, and the position errors differential equation is achieved through the kinematics model of the mobile robot; And then the observation model of the system is designed based on the trajectory tracking problem, through the connection between the predictive controller and the observation model of the system, the observed predictive controller is designed. Finally, under the environment of MATLAB, the simulation of trajectory tracking problem of the mobile robot under discontinuous stretch is made through the designed controller in this paper, and this simulation result is compared with the simulation result of PID controller. The simulation results shows that the controller is designed in this paper with good robustness, rapidity and stability, which could be used for the study of the trajectory tracking of the mobile robot.