A 50mm focal length, F/1.25, Gaussian type optical system is designed in this paper, which has 20°field of view. Actual star image adding optical cross-talk effect of CMOS(Complementary Metal Oxide Semiconductor), detector is simulated by non-sequential ray tracing in ZEMAX^® optical design and analysis software to evaluate its performance. The distortion relative to image spot centriod is introduced and calculated by simulated star images, which is less than 0.03% of lens in this paper. Thermal adaptability is discussed by opt-mechanic thermal analysis, which shows the RMS spot radius of marginal filed changes less than 0.7μm under 10°C temperature gradient, and changes less than 1μm during homogeneous temperature changing from -40°C to +40°C. The results of analyses and simulations show the design of this lens can achieve the requirement of high precision CMOS star sensor well.