a kind of space target acquisition optical system with small f-number was designed. the system had a working wavelength range of 0.45 similar to 0.85 mu m, an effective focal length of 240 mm, a field of view is 2 omega=3 degrees, and an f-number of f/2. the system characteristic is that the structure is simple. and the especial requirements of the spot, energy concentration, distortion and lateral color etc. are all satisfied. the primary and secondary mirrors are all spheres, so the difficulty and cost of machining are reduced. moreover, the temperature characteristic of the system is analyzed. the temperature request is satisfied.