With the rapid development of infrared technology, the concept of SWaP-C (small size, light weight, low power consumption and low cost) has been expanded from infrared detector to the whole design process of infrared thermal imager. In the design of uncooled continuous zoom infrared thermal imager, compared with the modularized uncooled detector and imaging circuit, the optical system affects its envelope size, product weight and price cost. A light, small, low-cost, high-performance uncooled infrared optical system needs to achieve the following five goals. First, the number of lenses is as small as possible. Second, the length of the optical system is short. Third, the diameter of the large objective lens is small. Fourth, the optical system has high MTF. Fifth, the optical system has good environment adaptability. Therefore, the design of an uncooled LWIR continuous zoom optical system with short length, light weight, low cost and high performance will have broad market prospects.There are difficulties in miniaturization and athermalization design of uncooled LWIR continuous zoom optical system due to its large relative aperture and few kinds of infrared optical materials. The purpose of compressing the total length of system and balancing aberration is achieved by using three groups of linkage zoom technology. Through the active compensation of athermalization technology, the system has good imaging quality in the temperature range of -40-60 ℃. The specific design process of the optical system is as follows. Firstly, the calculation program is compiled according to the three groups of linkage continuous zoom models. According to the design index, the initial optical form is calculated by considering the total optical length, lens focal length distribution and lens spacing. The parameters are input into Zemax optical design software to establish the ideal optical model. Secondly, the shape and material are reasonably selected according to the focal length of the lens, and the evaluation function is set to enter the optimization and global optimization. Thirdly, according to the results of the evaluation function, the imaging quality at normal temperature and at high and low temperature is evaluated. Then, the tolerance analysis of optical system is carried out to make the system meet the tolerance range of processing and assembly requirements. Finally, the optical system zoom curve renormalization operation is carried out to complete the optical system design. The design flow chart is shown (Fig.2).The final design result of the compact and low-cost uncooled LWIR continuous zoom optical system is shown (Fig.4). The whole system uses four lenses with the working band of 8-12 μm, the focal length range of 20.7-126 mm, the corresponding F# of 1.05-1.2, the field of view range of 21°×16.8°-3.5°×2.8°. The zoom ratio is 6.0×, the maximum machining diameter is 116 mm, the total length of the optical system is 180 mm, the total weight of the optical part is 418 g, and the telephoto ratio is 1.44. The MTF, SPT and distortion of the optical system are analyzed by Zemax optical simulation software. The system imaging is clear and meets the requirements. The MTF of the optical system at normal temperature (Fig.5), the SPT of the optical system (Fig.6). and the system distortion (Fig.7) are shown. The imaging quality of the optical system is evaluated at high and low temperature, and the optical system meets the requirements of athermalization. The tolerance of the optical system is estimated by statistical algorithm, and the tolerance of the system meets the actual use requirements. By renormalizing the cam curve of the optical system, the motion curves of the three lenses are obtained (Fig.15). The optical system achieves the SWaP-C goals. Based on a 640×512 uncooled focal plane detector with pixels size of 12 μm, a compact low-cost continuous zoom optical system composed of four lenses was designed using variable F# design method, three groups of linkage zoom design technology and active compensation for athermalization. The focal length of the system varies from 20.7 mm to 126 mm, the total optical length is 180 mm, the lens processing technology is mature, the processing and adjustment tolerance is good, the zoom cam curve is smooth, the cam track is easy to process, and the motion servo control is simple. The system has clear imaging in the environment of -40 ℃ to +60 ℃. The optical system has the characteristics of light weight, high performance and low cost. It will be widely used in unmanned equipment platform and handheld thermal imager equipment, and promote the development of uncooled infrared thermal imager in the direction of reducing SWaP-C.