According to a 640×480 uncooled detector with pixel size of 17 μm×17 μm, a long wavelength infrared varical optical system with varifocal ratio of 6× is designed with only 4 lenses. To meet the requirements of low cost and high transmission, an initial configuration is obtained through theoretical calculation. The aberration of the initial configuration is optimized by using the CodeV software. Finally, cam curve solution and image quality evaluation are carried out for the design result. The result shows that when the relative aperture of 1.4:1 is kept, the optical system can realize continuous zooming from 20 mm to 120 mm in the 8 to 12 μm waveband. The Modulation Transfer Function (MFT) at the spatial frequency of 20 lp/mm is greater than 0.5. It is found in the actual measurement of the prototype that the optical system has the features of large zooming ratio, compact configuration and high resolution. It is suitable for infrared monitoring systems.