Endoscopic surgery often requires sampling and resection of lesions in the unstructured narrow digestive tract, which puts high demands on the flexibility and precision of endoscopic surgery manipulators. For this reason, a novel cable-driven continuous endoscopic surgery manipulator prototype is proposed in this paper. Firstly, a Nested Kinematic Mapping System (NKMS) of “cable-driven cable length—kinematic joint angle—end-effector position” is established for the manipulator. Second, the nonlinear hysteresis effect of the cable was considered and compensated for the error in the kinematic model. The hysteresis model is parameterized by design measurement experiments. Finally, the model was validated by simulation experiments. The results confirm the validity of the kinematic model and the hysteresis model, which can meet the needs of endoscopic surgery. The advantages of this type of manipulator in terms of flexibility and precision in endoscopic surgery are demonstrated.