This paper focuses on the kinematic calibration problem for the general cable-driven serial manipulator (CDSM) with multi-segment cables to improve its motion control accuracy. Firstly, to fully describe the calibration parameters of cables, links, joint positions, and the transmission system, this paper proposes a new cable routing description method named cable-routing configuration struct (CRCS), which provides a complete set of parameters to be calibrated for the proposed self-calibration algorithm. Then, a self-calibration algorithm for CDSM with motor incremental encoders is proposed, which can calibrate the robot at one time only using sufficient measured motor and joint positions. Its premise, the initial cable length, needs to be calibrated. Finally, the parameters of a three-DOF (degree of freedom) six-cable CDSM were described using the CRCS description method, and a comparative experiment was carried out on the same motion controller using the parameters before and after calibration. The experiment results of trajectory tracking error showed that the calibration parameters obtained by the proposed calibration algorithm can significantly improve the motion control accuracy of the three-DOF six-cable CDSM. This verified the correctness and effectiveness of the proposed calibration algorithm.