According to the Schupmann’s achromatic theory, a calculation method of off-axis four-mirror diffractive imaging optical system is introduced. By using the method, an optical system which has an aperture of 1 m, F-number of 8, full field of view of 0.12°, waveband of 582.8 nm～682.8 nm is designed. The results show that the chromatic aberration is corrected effectively. The modulation transfer function (MTF) is more than 0.53 in the range of 50 lp/mm, and the RMS radius of diffusion spot is less than the airy radius. It demonstrates that the image quality of this system is close to the diffraction limit. It is analyzed that the processing of diffractive primary lens and diffrac-tive correct mirror can be realized by traditional lithography and diamond turning, respectively. Monte-Carlo simula-tion of tolerance analysis is carried out, it determined that the tolerance error mainly originates from the tilt angle of relay mirror, which provides guidance for the process of assembling and adjusting. This system has the advantages of broadband, high image quality, which can provide references for the development of reflective diffractive imaging optical system.