The energy properties and the differential cross-sections of laser-electron-Compton scattering are quantitatively investigated. The calculations show simple structures of the scattered photon energy and the angular distribution of the differential cross-section. At high incident electron energy, Compton scattering X-ray source has features of easily tunable photon energy and small forward emission angle. Although the dispersion of Compton scattering X-ray source is large, narrow bandwidth X-ray emission can be obtained experimentally by using specific monochromatic filter. The total cross-section and the cross-section within the forward emission angle （γ, where γ= E/m0c2 is the total electron energy （E） in the unit of its static energy （m0c2）） change slightly for different laser wave lengths and different incident electron energies in a broad range from 1 MeV to 10 GeV. They have values of 0067 mb and 0033 mb, respectively. The total cross-section of the visible lights is very small. These results may be useful for building new generation ultra-short X-ray source based on Compton scattering technique.