Based on the anti-parallelogram mechanism, an approximate cylindrical rolling joint is proposed to develop a novel cable-driven snake-arm robot with multiple degrees of freedom (DOF). Furthermore, the kinematics of the cable-driven snake-arm robot are established, and the mapping between actuator space and joint space is simplified by bending decoupling motion in the multiple segments. The workspace and bending configurations of the robot are obtained. The static model is established by the principle of minimum potential energy. Furthermore, the simplified cable constraints in the static model are proposed through Taylor expansion, which facilitates the equilibrium conformation analysis of the robot under different external forces. The cable-driven snake-arm robot prototype is developed to verify the feasibility of the robot design and the availability of the static model through the experiments of the free bending motion and the external load on the robot.