This paper presents the design, analysis, and development of a novel four degrees of freedom (4-DOF) endoscopic robot with cable-driven multisegment flexible continuum mechanisms. The endoscopic robot is mainly composed of the passive positioning arm, cable-pulley system, and 3-DOF flexible continuum mechanism. The forward and inverse kinematics of the endoscopic robot are derived based on the constant curvature assumption, and its working space, flexibility, and preoperative incision determination method are analyzed as well. Based on the hardware structure of the robot system, a control strategy and a control software are developed, and the continuum mechanism is kinematically calibrated to carry out the trajectory planning experiment and simulated surgery experiment. The experimental results show that the calibrated constant curvature model can be used for the motion control of the continuum mechanism, and the 4-DOF endoscopic robot can meet the visual field requirements of minimally invasive surgery.