This article reports a trajectory tracking control technique for snake robots with sideslip elimination and coefficient approximation. By introducing an integral part and virtual input variables to optimize the line-of-sight guidance law, a closed-loop trajectory tracking system with the functions of canceling disturbance and sideslip is designed. Besides, the method constructs the time-varying predicted values of virtual model variables and viscous friction coefficients to approximate the system's unmeasurable states. The approximation value can compensate for a snake robot's joint offset and torque input. Then, it is proved via the Lyapunov approach that the designed system is stable. The remarkable advantage of this strategy is that the accuracy of a snake robot tracking the ideal trajectory is optimized, which can improve the error's stability and the body's adaptability to the surroundings. The simulation and experimental results confirm the usefulness of the proposed technique.