Anamorphic optical systems have different focal lengths in X and Y direction, objective field of view (FOV) aspect ratio will not be restrained by detector aspect ratio, so it can enlarge the FOV or improve the target resolution in one direction while not affecting another direction. Design method of unobscured three mirror anamorphic optical systems is studied. Zernike aberration analytical method is used to analyze the aberration characteristics. Biconic Zernike surfaces of double curvature is used to correct the aberrations. A cooled mid-wave infrared optical system is designed at focal length in X direction of fx=100 mm, focal length in Y direction of fy=150 mm, F number of 2 with FOV of 3.3°×1.65°. The aspect ratio of the detector is 43 and the aspect ratio of the objective FOV is 21. The modulation transfer function of this system is above 0.61 all over the FOV at the Nyquist frequency of 33 lp/mm. Each reflective surface and the whole system are symmetric about the YZ plane. The result shows that this system can change the aspect ratio in objective FOV and enlarge the FOV in X direction with compact structure and favorable image quality.