In field operations of tracked chassis, due to the impact and noise caused by uneven ground, the trajectory tracking control accuracy is low and the stability is poor. In this paper, a trajectory tracking controller suitable for tracked chassis is designed based on the linear model predictive control algorithm. This method takes the chassis position as the state variable and the speed of the left and right track wheels as the control variable. A state deviation model is established based on the kinematic model of the tracked chassis, and the trajectory tracking control of the chassis is optimized and solved by constructing a quadratic programming problem with constraints, achieving optimal control. A controller simulation model was built using Matlab/Simulink, and the parameters of the MPC controller were analyzed by this model. It was found that the time domain has a significant impact on the tracking accuracy and real-time performance, and the weight coefficient has a significant impact on the control smoothness. The specific parameters of the MPC controller were further determined. Additionally, the controller performance was verified through simulation and field tests using the determined parameters. When traveling at a speed of 1 m/s, the average lateral error of the tracked chassis' field trajectory tracking was 4.41 cm, with a standard deviation of 4.50 cm. The average lateral error of the curve tracking was 9.83 cm, with a standard deviation of 10.57 cm. The average heading error of the straight line was 0.0306 rad, with a standard deviation of 0.0382 rad, and the average heading error of the curve tracking was 0.0646 rad, with a standard deviation of 0.0911 rad. The test results show that the MPC controller designed in this study can achieve precise and stable tracking of complex trajectories in unmanned tracked chassis field operations.