Due to the nonlinear friction in wire/cable transmission system, the elongation of the drive cable and the coupling between adjacent joints, the motion control accuracy of the continuum robot is low. So an error compensation method of the continuum robot with considering of the nonlinear friction was presented. Firstly, the kinematics model of the robot was established by the Euler transformation principle under the constant curvature arc assumption, and then the statics model of the continuum manipulator, including the coupling between adjacent joints was derived based on the principle of virtual work. Moreover, the influences of the pretightening force of the cable and different wrap angle on the force transfer efficiency of the cable transmission system were analyzed by the experiments. By using the improved Capstan equation, a force transferring model considering the bending stiffness of the cable and the nonlinear friction was established, and the model-based error compensation method was presented. Finally, the effectiveness and correctness of the established model and control method were verified by the motion compensation experiments of the continuum manipulator. The results indicated that the motion control accuracy of the robot after compensation was significantly improved compared with that before compensation, the average position error was reduced from 5.94mm before compensation to 3.15mm after compensation, and the compensation rate was up to 46.97%, which verified the correctness of the compensation method and the proposed model.