This paper presents a multi-mode control strategy for precise trajectory tracking of snake robots. The strategy integrates head-direction control, PD control, and curvature optimization control to achieve efficient and smooth path tracking. Compared to traditional path-tracking methods, the proposed approach demonstrates significant advantages in global orientation adjustment, local deviation correction, and overall morphology optimization. The head-direction control provides global orientation adjustment capability, ensuring the robot can quickly align with the target. Trajectory error control dynamically corrects local deviations, effectively eliminating cumulative errors in complex paths. Curvature optimization control adjusts the overall morphology, allowing the robot to maintain smooth and natural motion on curved paths. The synergistic effect of multi-mode control not only enhances the adaptability, smoothness, and precision of trajectory tracking but also exhibits stronger robustness and stability in dynamic and complex environments. Simulation results show that the proposed method achieves efficient and accurate trajectory tracking in various complex environments, demonstrating broad application prospects.