In order to increase the searching efficiency and detection probability,more and more Focal Plane Detectors are used in infrared searing or surveillance systems. The optical image must be static to detector for a period of time to reach the demand ratio of signal to noise,therefore a compensation for image motion must be applied. The optical compensation which is commonly used exploit a wiggling mirror or transparent plane after a telescope to compensate the imaging motion generated by platform rotation. An optical system of infrared telescope that the image field of view correlated linearly with the objective field of view is described in this paper,and the wave band of the optical system is 7.7～10.3 μm with magnification of 10×.The telescope can be used in infrared searching system,where a wiggling mirror or transparent plane is used for compensating the imaging motion generated by platform rotation. The calculating results show that the residual image motion is less than 1 μm in the whole field of view.