Aiming for the fine observation of fast physical phenomena such as phonon propagation and laser ablation, phase-contrast X-ray imaging combined with a crystal X-ray interferometer and the X-ray free-electron laser (XFEL) of the SPring-8 Angstrom Compact Free-Electron Laser has been developed. An interference pattern with 70% visibility was obtained by single-shot exposure with a 15 keV monochromated XFEL. In addition, a phase map of an acrylic wedge was successfully obtained using the fringe scanning method.