The compound refractive X-ray lens (CRL) for focusing hard X-rays is investigated to determine the parameters such as the focal length, the focal spot size, and spatial distribution at the focal spot using a simple theoretical calculations and CRLs fabricated by the self-assembly method. The number of individual compound lenses are defined for the given focal length of 1 m. The X-ray energy of 1 to 40 keV is used in the calculations. The CRL for focusing hard X-rays which generated from the X-ray tube is fabricated by nanoparticle-polymer composite in the form of circular concaves. The self-assembly method is applied to form the nanoaluminum-poly (methly meth-acrylate) composite and carbon-polymer composite CRL lenses. Aluminum nanoparticles of 100 nm and carbon microparticles are diffused in the polymer solution then the high gravity up to 6000G is applied in it to form the concave lens shape. X-ray energy at 8 keV is used for characterization of the composite CRLs. The FWHM of intensity for the fabricated nanoaluminium composite CRL system, N=10 is measured as 1.8 mm, which would give about $70{mu}m$ in FWHM at 1 m of the focal length.