In off-road environments, vehicles often have to deal with much more rugged and uneven terrain. To address the insufficient performance of existing control methods for vehicle trajectory tracking on nonplanar surfaces, this paper designs a trajectory tracking controller based on Nonlinear Model Predictive Control, which utilizes the nonplanar kinematics and dynamics models established in this paper to enhance the model accuracy. Additionally, considering the complexity of the nonplanar vehicle model, this paper proposes an optimization strategy based on the real-time iteration to alleviate the computational pressure. In subsequent experiments, the designed controller is compared with a flat controller and a fully iterative nonplanar controller. The experimental results show that the controller designed in this paper demonstrates an enhancement in control accuracy when compared with the flat controller. Moreover, while sacrificing only a small amount of accuracy compared with the fully iterative controller, it substantially reduces the computational time.