This paper proposes a novel path planning method for a robot to climb on the deformable clothes surface. Based on the deformable characteristic of the clothes, the tension force of clothes is analyzed and the model of tension degree is established. A clothes climbing robot called Clothbot is composed of a two-wheeled gripper and a 2 Degrees of Freedom (DOF) tail. Based on the locomotion of this robot, the weights of tension degree and the locomotion characteristic are added into the A* algorithm. Combined with the two weights applied, the optimal path to the target for the Clothbot is obtained. The Clothbot has been developed to evaluate the algorithm. The simulation and the experiments have verified the feasibility of this method. In addition, The error state of the movement of the robot which is called side tumbling has been corrected by the motion of the 2-DOF tail.