In order to improve the detection accuracy and range of new generation of Forward Looking Infra-Red (FLIR) system for distant targets, its optical system, which usually consists of a fore afocal telescope and rear imaging lenses, is required to has wide spectral range, large entrance pupil aperture, and wide field of view (FOV). In this paper, a new afocal Three-Mirror Anastigmat (TMA) with widened field of view and high demagnification is suggested. Its mechanical structure remains coaxial, but it has zigzag optical axis through properly and slightly decentering and tilting of the three mirrors to avoid its secondary obscuration due to the third mirror as FOV increase. Compared with conventional off-axis TMA, the suggested zigzag-axis TMA is compact, easy-alignment and low-cost. The design method and optimum result of the suggested afocal TMA is presented. Its initial structural parameters are determined with its first-order relationship and primary aberration theory. Slight and proper decentration and tilt of each mirror is leaded in optimization so that its coaxial mechanical structure is held but attainable FOV and demagnification are respectively as wide and as high as possible. As an example, a 5.5-demagnification zigzag-axis afocal TMA with a wavelength range, an entrance pupil diameter, and FOV respectively from 3μm to 12μm, of 320mm, and 2×3.2 degrees and with a real exit pupil, is designed. Its imaging quality is diffraction limited. It is suitable for fore afocal telescope of the so-called third generation FLIR.