To track and control the trajectory of a Wheeled Mobile Robot (WMR) in the smooth, robust and stable modes, the principle of the bio-inspired dynamics was analyzed, the nonlinear Model Predictive Control (MPC) was explored and a MPC approach based on bio-inspired dynamics was proposed. Firstly, a bio-inspired dynamics sub-controller was proposed based on the neurons′ excellent ability in information processing to overcome the velocity jump issue in the traditional control method. Then, an optimal sub-controller consisting of a cost function and four constraints was obtained based on the MPC principle. Finally, a terminal region and a terminal sub-controller were designed to stabilize the whole control system. Simulation results with the proposed control method indicate that the converge time of the WMR system to the reference trajectory has reduced from 12 to 5 s and the ranges of the initial linear and angular velocities are narrowed from ［-3, 4］ m/s and ［-5, 6］ rad/s to ［0, 2］ m/s and ［-3, 3］ rad/s, respectively. The output of the system is smooth and bounded, fulfilling global asymptotic stability as well as higher tracking precision. As the algorithm used in derivation is not be limited by the WMR kinematics model, it can be used in other types of mobile robots.