Although X-ray grating-based phase contrast imaging enables to obtain high image contrast of weekly absorbing substance, the imaging time is too long, due to high resolution detector. Furthermore, the imaging energy is usually about 30 keV, because of the limitation of grating manufacturing technique. In this paper, the requirement of grating manufacturing technique was relaxed sharply, thus the imaging energy was increased, based on the principle of projection imaging. In addition, fast phase contrast computed tomography (CT) imaging was realized on account of cycle-step-cycle mode, using medical CT tube source and medical detector. Experiments were carried out with tube voltage 80 kV, tube current 180 mA and 80 s exposure time to substance on the imaging system at National Synchrotron Radiation Laboratory. Last, how to improve the density resolution of the imaging system was discussed.