As the number of initial structures is not enough for optical designers need, it is significant that methods of freeform surface are studied, because freeform surface is able to eliminate aberrations greatly. The design methods of initial structures are usually ray tracing or numerically solving of differential equations to construct point clouds, it is complex and costing largely of computing. A new method deriving the formulas of freeform surface in a view that optical system changes wave front was presented, and an infrared off-axis optical system with large relative aperture and wide working spectrum 3~12μm, focal length is 300mm, F/2.5, full field of view is 2.04°×2.56° was designed using this method. This system is with high quality of image (diffraction limit) and 100% cold stop efficiency, 0.059λ@3.67μm average RMS wavefront error.