A 10× mid-wavelength infrared (MWIR) continuous zoom optical system is designed for cooled 320 pixel×240 pixel staring focal plane array detector. The system uses mechanical positive compensation zoom system. 100% cold stop efficiency is realized by secondary imaging system. Two common infrared optical materials, i.e., silicon and germanium, are used. By introducing reasonable aspheric and diffractive surfaces, the aberrations are balanced. By using ZEMAX optical design software, the system is optimized for continuous zoom is the range of 20~200 mm. After design and optimization, the system only uses 7 lenses to realize 10× continuous zoom. The F number is 2, the working wavelength is 3.7~4.8 mm, the modulation transfer function (MTF) at spatial frequency of 16 lp/mm is larger than 0.4, and the root mean square (RMS) radius is smaller than 16 mm. It has a resolution close to diffraction limit and satisfies the requirement of imaging. Moreover, the system has a smooth curve zoom and meets the zoom requirement.