Catadioptric null compensation test is a novel concave aspheric mirror testing method which combines the advantages of Offner refractive and Maksutov reflective compensation test. Its compensation ability is strong and testing optical path is compact. Non-spherical test with large aperture and large relative aperture is a difficult problem to restrict the improvement of its processing quality. In view of a concave paraboloidal reflector whose aperture is 4 m, eccentricity ratio is 1, and vertex curvature radius is 16 m, a catadioptric null compensator is designed. Based on the third-order aberration theory, the arrangement and calculation of the compensator initial structure is carried out. The initial structure parameters are optimized with Zemax, and the finial structure of compensator is obtained. The axial size of testing optical path is about 12 m. The residual wave phase error is 0.005λ after system optimization. The design and simulation results show that the catadioptric null compensator is very advantageous for the processing and testing of large aperture concave aspheric mirrors.