The certification is performed through directly testing the computer-generated hologram(CGH) which is used to synthesize the wavefront reflected by a perfect primary mirror. If the errors of computer-generated hologram are within the requirement, the certification can be realized. The principle and methods of certification by computer-generated hologram are introduced ,and its errors are analyzed. Using the computer-generated hologram written by electronic beam lithography, the compensator for 850 mm F/2 parabolic mirror is certified, and the standard aspherical precision created by the compensator is not less than the primary mirror precision synthesized by computer-generated hologram, the root mean square(RMS) error is 0.012λ. The results show that it's an effective way to certify the compensator by simulating the wavefront reflected by perfect primary with computer-generated hologram. Combining the sophisticated lithographical manufacturing technology, high-precision certification can be achieved.