Based on a 640x512 cooled staring focal plane array(FPA) detector, pixel size 15 mu mx15 mu m, a long focal length mid-wavelength infrared optical system was designed. In this paper, the working wavelength is 3 mu m similar to 5 mu m, the temperature range is -30 degrees C similar to+50 degrees C, this system can realize 1000mm focal length, the F-number is 4, the full field of view is 0.70 degrees, satisfy 100% cold shield efficiency. A re-imaging refractive system was adopted in this designed optical system consists of a main objective group and a projection group. First of all, the structural selection and the initial parameter calculation were introduced. Secondly, on the basis of variety of the temperature, a focusing len was presented in this system to adjust to produce a clear image. Last but not the least, to improve image quality and environment adaptability, the analysis of temperature change and ghost image were described particularly. The design results prove that at the spatial frequency of 33 lp/mm, the axis MTF of the optical system is greater than 0.35, the system can offer a high resolution and excellent images, and it has the advantages of good adaptability, simple structure, easy to adjust, and high transmittance.