Because of redundant freedoms, designing a robust any path following controller for snake-like robots is very challenging. In this paper, a novel path following controller, combining the robust following controller used in the unicycle robot and the fiber bundle model of snake-like robots, is proposed to follow any planar curve. More specifically, firstly, the kinematic model is established based on the fiber bundle theory which connects snake-like robots and unicycle robots. Then the robust path following controller for the unicycle robots is modified to be applied to the sake-like robots. Finally, to obtain a feasible controller, an estimation method for the orientation angle of the robot in the fiber bundle is proposed. To validate the proposed method, numerical simulations and experiments are performed. The results demonstrate that the proposed following controller is robust and valid.