Three-dimensional spiral gait enables a snake robot to climb over obstacles, cross caves, and adapt to complex environments. This paper reports an anti-disturbance path-following control method for a snake robot with a spiral gait. This method reduces the deviation of the robot's position in following the ideal path by estimating the time-varying parameters, the external disturbances, and the viscous friction coefficients. The estimations are used to compensate for the control inputs of the system, which can improve the adaptability of the robot to the environment. Then, the attitude and position errors can rapidly converge to the origin. An appropriate Lyapunov function is adopted to explore the stability of following errors. Experimental results show that the proposed method can accelerate the convergence rate of errors, reduce the fluctuation peak, and improve the following stability of snake robots.