The mobile robot kinematic model is a nonlinear affine system, which is constrained by velocity and acceleration limits. Therefore, the traditional control methods may not solve the tracking problem because of the physical constraint. In this paper, we present the nonlinear model predictive control (NMPC) algorithm to track the desired trajectory based on neural-dynamic optimization. In the proposed algorithm, the NMPC scheme utilizes a new neural network named the varying-parameter convergent differential neural network (VPCDNN) which is a Hopfifield-neural network structure with respect to the differential equation theory to solve the quadratic programming (QP) problem. The new network structure converges to the global optimal solution and it is more efficient than traditional numerical methods. In the simulation, we verify that the proposed method is able to successfully track reference trajectories with a two-wheel mobile robot. The experimental validation has been conducted in simulation and the results show that the proposed method is able to precisely track the trajectory maintaining a high robustness based on the VPCDNN solver.