Dark-field radiography of the human chest is a promising novel imaging technique with the potential of becoming a valuable tool for the early diagnosis of chronic obstructive pulmonary disease and other diseases of the lung. The large field-of-view needed for clinical purposes could recently be achieved by a scanning system. While this approach overcomes the limited availability of large area grating structures, it also results in a prolonged image acquisition time, leading to concomitant motion artifacts caused by intrathoracic movements (e.g. the heartbeat). Here we report on a motion artifact reduction algorithm for a dark-field X-ray scanning system, and its successful evaluation in a simulated chest phantom and human in vivo chest X-ray dark-field data. By partitioning the acquired data into virtual scans with shortened acquisition time, such motion artifacts may be reduced or even fully avoided. Our results demonstrate that motion artifacts (e.g. induced by cardiac motion or diaphragmatic movements) can effectively be reduced, thus significantly improving the image quality of dark-field chest radiographs.