Zero-power corrector can be applied in two-mirror system to enhance aberration correction ability or avoid using aspheric optics. There are seven variables in this kind of system, which is helpful for aberration correction and has no chromatism. Based on the third-order aberration theory, normalized method and paraxial function, the aberration characteristic of systems with a zero-optical power corrector which located in front of the mirrors is analyzed, and kinds of third-order aberration correction formula are given. The analysis is confirmed by a design sample with optical design software. It will greatly benefit optical designer for the design of this kind of system.