The parabolic compound X-ray refractive lenses are a kind of novel optical components, especially suitable for hard X-rays. Due to their parabolic profiles they are free of spherical aberration and are proper devices for sub-micrometer focusing and imaging. The focusing performance of the parabolic compound X-ray refractive lenses is studied theoretically and experimentally in this paper. Firstly, the derivation of the exact focal length formula using matrix optics method and a criterion of the thin lens approximation are described. And the intensity distribution near focus, limiting focal spot size, effective aperture and transmittance are deduced based on the diffraction theory. Several parabolic compound X-ray refractive lenses with PMMA material were fabricated by means of deep X-ray lithography. Then the X-ray microbeam experimental system was built on the 4W1A beamline of Beijing Synchrotron Radiation Facility （BSRF） based on the parabolic compound X-ray refractive lenses we fabricated. The focusing performances of three PMMA parabolic compound X-ray refractive lenses were measured and analyzed under 8 keV monochromatic X-rays. According to the experimental results, it is concluded that the PMMA parabolic compound X-ray refractive lenses promises good hard X-ray focusing performance.