A five-axis white-light interference-measurement system is constructed by integrating a self-developed coherence scanning interferometric probe into a Moore five-axis motion platform for the surface-morphology measurement of curved optical components. To achieve automated measurement, the kinematic model of the system is investigated and the inverse kinematic equations are solved. A calibration method using high-precision aspherical calibration components with known expressions is proposed for unknown parameters in the inverse kinematics equations. Finally, an experiment to verify the calibration accuracy of the proposed system is conducted, and the results show that after automatic focusing and leveling, the error between the actual and theoretical focal coordinates remains less than ±3 μm. The measurement requirements of the probe is satisfied, and the proposed system can automatically measure the surface morphology of curved optical components.