In order to increase spatial resolution, five-mirror afocal optical system with axial-symmetric primary mirror was designed, which was used for principal system of image space scanning system. The system was well compact and axial-symmetrical. The method of five mirror afocal system design based on primary aberration was explored. The structural parameters were calculated according to magnification and obscuration ratio of each mirror. The conic parameters were calculated according to primary aberration coefficient. The procedure for calculating initial structural parameters was programmed. Then a five-mirror afocal system was designed with an entrance pupil diameter of 1 m, a field of view of 5°×0.1°, the operating wave band of 8-10 μm, compression ratio of 10 times. The results indicate that the maximum root mean square (RMS) wavefront error is less than 0.065λ(λ=9 μm), the maximum optical path difference(OPD) is less than λ/4(λ=8-10 μm). It has high imaging quality and the modulation transfer function (MTF) is approached to the diffraction limit. The method of afocal system design can be widely used for high spatial resolution multichannel imaging.