The X-ray compound lens is a novel optical device that focuses X-ray radiation by refraction effect. The theoretical and numerical study of such a device is reported, including the derivations of the diffractive screen function of the compound lens and the equations of the intensity distribution in the focus plane by considering both refraction and absorption effect and diffraction theory. The first-order and the second-order origin moments are used to describe the optical performances of the device at the image plane. This theoretical method can be easily generalized to the case of the compound X-ray lens with a double-concave shape. The structural parameters of an X-ray compound lens with Al material are designed. The second-order central moment of the intensity distribution at the image plane and dependence of the radiation intensity at the focus on the structural parameters of the compound lens are analyzed by using numerical calculationm at the focal plane after X-ray radiation passes the compound lens is calculated as X-ray raidation energy is 0.93 keV, 9.89 keV and 29.78 keV, respectively.