X-ray imaging is of paramount importance for clinical and preclinical imaging but it is fundamentally restricted by the attenuation-based contrast mechanism, which has remained essentially the same since Roentgen's discovery a century ago. Recently, based on the Talbot effect, groundbreaking work was reported using 1D gratings for X-ray phase-contrast imaging with a hospital-grade X-ray tube instead of a synchrotron or microfocused source. In this paper, we report an extension using 2D gratings that reduces the imaging time and increases the accuracy and robustness of phase retrieval compared to current grating-based phase-contrast techniques. Feasibility is demonstrated via numerical simulation.