This paper develops a disturbance rejection model predictive control (MPC) scheme for tracking nonholonomic vehicle with coupled input constraint and matched disturbances. Two disturbance observers (DOBs) are designed to estimate the unknown disturbances and the disturbances with known harmonic frequencies, respectively. By combining the DOB with MPC, a compound controller is presented. Recursive feasibility of the optimization problem is guaranteed by tightening the terminal region and the input constraint. We show that the system is input-to-state stable if no information about the disturbance is available and can reach an offset-free tracking performance if the harmonic frequencies of the disturbance are known. Finally, simulations and experiments are provided to show the efficiency of the proposed approaches.