Stearns' scattering method is introduced in this paper, which describes the scattering of a single non-ideal interface and is applicable for soft X-ray short wavelength region. It is then extended to multi-layer structure and uses a mathematical modal from Stearns' method to describing the multi-layer interface roughness at soft X-ray short wavelength region (1～10nm). Under the framework of this theory, the interface roughness of a Co/C multi-layer mirror with the wavelength of 4.77 nm is analyzed. The root-mean-square roughness of the multi-layer interface of the mirror is 0.7 nm.