Abstract: The high-qualified optical systems which are used in imaging spectrometers must have some advantages, such as large linear FOV, large relative aperture, wide-spectral imaging, light weighted, etc, which makes the off-axis all reflective optical systems an important research direction in this field. A method for the design of off-axial reflective 3-mirror optical system with large linear field of view(FOV) and large relative aperture was described in this paper. The method was based on the 3rd-order aberration theory. After the constrained optimization of a set of Seidel aberration coefficient functions, the designer could achieve the initial construction parameters of the optical system, i. e. the radii and separations of lenses. And during the designing process, decenters and tilts of mirrors were adjusted continuously to eliminate the obscurations under the premise of assurance of image quality. In the end, the design results were given, and the MTF curves prove the feasibility of this method.