Prospective right hemidiaphragm navigator (NAV) is commonly used in free-breathing coronary MRI. The NAV results in an increase in acquisition time to allow for resampling of the motion-corrupted k-space data. In this study, we are presenting a joint prospective-retrospective NAV motion compensation algorithm called compressed-sensing motion compensation (CosMo). The inner k-space region is acquired using a prospective NAV; for the outer k-space, a NAV is only used to reject the motion-corrupted data without reacquiring them. Subsequently, those unfilled k-space lines are retrospectively estimated using compressed sensing reconstruction. We imaged right coronary artery in nine healthy adult subjects. An undersampling probability map and sidelobe-to-peak ratio were calculated to study the pattern of undersampling, generated by NAV. Right coronary artery images were then retrospectively reconstructed using compressed-sensing motion compensation for gating windows between 3 and 10 mm and compared with the ones fully acquired within the gating windows. Qualitative imaging score and quantitative vessel sharpness were calculated for each reconstruction. The probability map and sidelobe-to-peak ratio show that the NAV generates a random undersampling k-space pattern. There were no statistically significant differences between the vessel sharpness and subjective score of the two reconstructions. Compressed-sensing motion compensation could be an alternative motion compensation technique for free-breathing coronary MRI that can be used to reduce scan time.