This paper presents a finite-time sideslip differentiator-based line-of-sight (LOS) guidance method for robust path following of snake robots. Firstly, finite-time stable sideslip differentiator and adaptive LOS guidance method are proposed to counteract sideslip drift caused by cross-track velocity. The proposed differentiator can accurately observe the cross-track error and sideslip angle for snake robots to avoid errors caused by calculating sideslip angle approximately. In our method, the designed piecewise auxiliary function guarantees the finite-time stability of position errors. Secondly, for the case of external disturbances and state constraints, a Barrier Lyapunov function-based backstepping adaptive path following controller is presented to improve the robot's robustness. The uniform ultimate boundedness of the closed-loop system is proved by analyzing stability. Additionally, a gait frequency adjustment-based virtual velocity control input is derived to achieve the exponential convergence of the tangential velocity. At last, the availability and superiority of this work are shown through simulation and experiment results.