Laser-Compton scattering is a promising method for generating high-brightness, ultrashort, energy-tunable X-rays. We have developed a compact X-ray source using laser-Compton scattering. Hard X-rays, ranging from 15 keV to 34 keV, were generated with a low-emittance, 38 MeV, 0.8 nC electron accelerator and a femtosecond 4TW Ti:sapphire laser. The created X-rays were composed of 2×106 (5×105) photons/pulse for interaction angles between an electron bunch and a laser pulse of 165° (90°). A highly accurate timing synchronization scheme was employed, and the fluctuation of the generated X-rays was suppressed to 11% (rms) for the 90° scattering. The spatial (angular) distributions for the intensity and the energy of the generated X-ray were measured, and agreed well with theoretical calculations. Thus, X-ray imaging has been demonstrated using a phase-contrast technique with the interference of an X-ray beam.