As a specific task for unmanned tracked vehicles, leader-following imposes high-precision requirements on the vehicle’s motion control, especially the steering control. However, due to characteristics such as the frequent changes in off-road terrain and steering resistance coefficients, controlling tracked vehicles poses significant challenges, making it difficult to achieve stable and precise leader-following. This paper decouples the leader-following control into speed and curvature control to address such issues. It utilizes model reference adaptive control to establish reference models for the speed and curvature subsystems and designs corresponding parameter adaptive control laws. This control method enables the actual vehicle speed and curvature to effectively track the response of the reference model, thereby addressing the impact of frequent changes in the steering resistance coefficient. Furthermore, this paper demonstrates significant improvements in leader-following performance through a series of simulations and experiments. Compared with the traditional PID control method, the results shows that the maximum following distance has been reduced by at least approximately 12% (ensuring the ability to keep up with the leader), the braking distance has effectively decreased by 22% (ensuring a safe distance in an emergency braking scenario and improving energy recovery), the curvature tracking accuracy has improved by at least 11% (improving steering performance), and the speed tracking accuracy has increased by at least 3.5% (improving following performance).