On the basis of a 384×288 uncooled staring focal plane array detector with pixel size of 25 μm, a 20-fold uncooled long wavelength infrared continuous zoom optical system is designed. The operation waveband of the system is 8～12 μm and its F number is 1.3. It has the advantages of larger relative aperture, higher zoom ratio and smooth zoom path etc. The system consists of seven lenses which are made from a combination of two kinds of materials. Most of the lenses are made from common germanium material so as to reduce the use of expensive materials and be easy for processing. By using one diffraction optical element and two aspheric elements, a compact structure of the system is realized. The system has its Nyquist spatial frequency of 20 lp/mm, Modulation Transfer Function (MTF) greater than 0.4 for short focus and long focus and MTF greater than 0.58 for middle focus. These MTF values show that the system has excellent image quality.