The present invention discloses an omni-directional mobile robot trajectory tracking method based on a numerical acceleration control. The method comprises a step of carrying out physical modeling onan omni-directional mobile robot, a step of setting a sampling period and establishing a discrete dynamic model of the omni-directional mobile robot, a step of setting a target trajectory and calculating driving force acted on each omni-directional moving part based on the numerical acceleration control so as to make the omni-directional mobile robot to track the target trajectory, a step of constructing a discrete state feedback system of an omni-directional mobile robot tracking error and calculating optimal parameters of a numerical acceleration controller for realizing the trajectory tracking, and a step of importing future information of the target trajectory and designing the numerical acceleration controller which can further improve the trajectory tracking precision. According to trajectory tracking control method of the present invention, the high-precision trajectory tracking can be realized even under the real-time change of ground friction force borne by each omni-directional moving part, and the method has good robustness.