A compact space optical system without moving parts which can get two focal lengths is designed. Ritchey-Chrétien (R-C) mirror is common for long-focus system and short-focus system. A splitter prism is used for splitting the light into two beams relayed by transmitting optical system. The focal length is 4700 mm and F number is 13.4 for the long-focus system, and the focal length is 2350 mm and F number is 6.7 for the short-focus system. Some measure is taken to make sure the less degradation of MTF for thermal distortion, such as a kind of material with small thermal expansion using comrection between the primer mirror and the second mirror and material with good thermal property as mirror substrate for reduce surface distortion. The modulation transfer function (MTF) of optical system in condition of (19±3) ℃ is analyzed, which shows a good result for user′s requirement.