Aspheric mirrors commonly utilize a zero position compensator along with an interferometer for surface shape detection. Therefore, the machining and assembly accuracy of the zero position compensator play a crucial role in determining the reliability of the detection results. This paper introduces a universal compensation error calibration method based on computer generated hologram (CGH). To test the method, a Φ856 mm,f/1.54 hyperboloid mirror is employed as the target aspheric mirror. First, a reflective CGH is designed, and the phase function of the CGH is determined using a ray tracing method. This ensures that the introduced spherical aberration is the same as the normal aberration of the aspheric main mirror to be tested. Subsequently, the correctness of the design is confirmed through ZEMAX simulation calculation, and the primary hologram is processed based on the phase function. Holographic strips are designed and processed on the same glass substrate for adjusting the calibration optical path. The experimental results demonstrate that the CGH calibration achieves a zero position compensator accuracy of λ/80. The proposed method is applicable to concave aspheric mirrors with large apertures and fast focal ratios. Consequently, it can serve as a reliable guide for calibrating zero position compensators in most positive axis aspheric mirrors.