Computer-generated hologram (CGH) is an effective way to compensate wavefront aberration in null test of aspheric surfaces and freeform surfaces. Our strategies of CGH design for 820mm diameter tertiary mirror surface figure testing are presented, and an experiment demonstrating the compensation test results of CGH is reported. We design a CGH including two sections on the same substrate in order to align the CGH to the incident wavefront: main section for compensating wavefront in null test, alignment section for adjusting the relative position between CGH and interferometer. Because there is no center hole in the mirror, in order to isolate different orders of diffraction, we used tilt carrier to make different orders of diffraction come to focus at different position perpendicular the axis to avoid ghost reflections. © 2019 SPIE.