A mid-wavelength continuous zoom optical system was presented for a staring Focal Plane Array(FPA) infrared detector by cooling assembly. The optical system with an optical configuration of reflect mirror fold was composed of a zoom object lens system and a secondary imaging system including seven lenses and two reflectors. On the basis of zoom principles, the systemic structure and design parameters were given by using special optical design software, then the schematic diagram and imaging quality were investigated. Finally, the performance and indexes of the system were verified. The results indicate that the system can offer a 50-500 mm continuous zoom and 100% cold shield efficiency. Moreover, the Modulation Transfer Function (MTF) in whole fields at Nyquist frequency is over 0.35 and the whole field distortion is below 2%. These results show that the system is characterized by high resolution, thermal sensibility, excellent images and smooth zoom locus.