This paper studies a model predictive hybrid tracking control scheme under a multiple harmonics time-varying disturbance observer for a discrete-time dynamics nonholonomic autonomous mobile robot (AMR) with external disturbance. To solve the robust tracking control problem of the AMR and unmanned aerial vehicle (UAV) air-ground cooperative, a hybrid tracking control strategy combined with improved model predictive control (MPC) method and multiple harmonics time-varying disturbance observer is presented. Firstly, a time-varying air-ground cooperative tracking control model based on the nonholonomic constraints AMR and quadrotor is established by polar coordinate transformation. Secondly, for external disturbances estimating and solving in practical engineering, a discrete-time multiple harmonics time-varying disturbance observer is designed. A hybrid tracking control scheme of the AMR based on the estimated states and MPC method with kinematics constraints is proposed, and a relaxing factor is designed to restrain the jump phenomenon of the MPC increment. Finally, experimental results are shown the effectiveness of the proposed control strategy.