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X-ray phase-contrast imaging (XPCI) is a versatile technique with wide-ranging applications, particularly in the fields of biology and medicine. Where X-ray absorption radiography requires high density ratios for effective imaging, XPCI is more sensitive to the density gradients inside a material. In this letter, we apply XPCI to the study of laser-driven shockc waves. We used two laser beams from the Petawatt High-Energy Laser for Heavy Ion EXperiments (PHELIX) at GSI: one to launch a shock wave and the other to generate an X-ray source for XPCI. Our results suggest that this technique is suitable for the study of warm dense matter (WDM), inertial confinement fusion (ICF) and laboratory astrophysics.