Lateral control is an important part in the system of driverless mining trucks, which is used to realize accurate tracking of planned path. To solve the problem of poor accuracy of the existing single point preview algorithm, firstly, the lateral error model and the simplified truck dynamics model were built. The established truck dynamics model was verified and compared by simulation. The results show that the truck dynamic model in this paper retains accurate even at higher speed. Secondly, against the time delay of truck steering system, the cascade LQR-PID controller and MPC-MRAC controller are designed. The former resists the disturbance of steering time delay through the inner PID loop, while the latter realizes the adaptive control by establishing the steering model. Then, the dual-shift condition simulation was carried out by co-simulation model, and two controllers were compared and analyzed. The results show that the designed two controllers have good performance in the steering lag system. Finally, the LQR-PID controller was applied to the field test at speed 30km/h. The test results show that, compared with the single point preview algorithm, the LQR-PID controller obviously reduced the max tracking error from 1.125m to 0.792m and mean error from 0.644m to 0.236m, which achieved the desired effect.