The omnidirectional mobile robot with 3-degree-of-freedom in the plane has high flexibility and can be also applied in crowded and narrow environment. The BP (backpropagation) neural network method is used to solve the problems of the vibration phenomena and trajectory error of the MY2 wheel developed in the laboratory during movement. According to the structure and movement characteristics of the robot, the BP neural network model is established and the parameters of the BP neural network are optimized. Trajectory simulation experiments based on the BP neural network model are conducted. The impact of initial values, different speeds and different trajectories on model are analyzed. The consequence shows that the method based on the suitable BP neural network can keep the trajectory error within the range of 3 mm and the deflection angle error less than 3°, so the BP neural network can decrease the robot vibration and improve the trajectory accuracy. The universal applicability of the BP neural network model is verified by inputting different motion trajectories, and the correctness of simulation results are validated by experiments in the end.