The primary mirror of a two-reflective system for a telescopy was replaced by a Golay 3 sparse aperture to reduce its weight and volume while remaining high angular resolution. Firstly, the two-reflective system with a spherical primary mirror and a hyperbolic secondary mirror was designed according to the third-aberration theory. Then, the primary mirror was substituted by a Golay 3 sparse aperture, and the relationship between fill factor and sub-mirror radius was analyzed. The whole system was simulated by Zemax software to obtain the Modulation Transform Function(MTF) and the spot diagram of the system . Finally, two silicon correcting lenses were inserted behind the secondary mirror to optimize the radius of the correcting lens and imaging distances and to improve the field of the system. By Zemax simulation, it is shown that the cutoff frequency of the system has been decreased from 114.5 lp/mm to 97.7 lp/mm and to 77.8 lp/mm as the fill factor reduces from 22.2% to 15% and to 10%, respectively. Moreover, inserting the correcting lens in front of the image plane can greatly enlarge the field of the system, which shows the RMS value of maximum spot radius without correcting lens is about 2.5 times larger than that with a correcting lens in the field of 0.3°.