With the development of space technology,the optical system design must be satisfied with the lastest demand due to the ground sample distance (GSD) steadily improving. The issues of the optical system design is discussed,the space optical system design principle with large F number,long focal length is analyzed and a reflective optical system which is characterized by the spectrum band 500-800 nm,focal length of 7200 mm and F number of 14.4 is designed. The result indicates that the field angle reaches 1.6°,the ground width reaches 12.5 km and the graund sample distance (GSD) reaches 0.62 m at 450 km orbit,the quality of image approaches the diffraction limited,modulation transfer function (MTF) reaches 0.38 at the Nyquist frequency of 50 lp/mm with 6% central obscure,and optical system distortion is less than 0.5%. So this kind of optical system can meet the demand for the use of high resolution space cameras. At the same time,the large F number,long focal length design principle are approved.