Dynamic contrast-enhanced MRI of the heart is well-suited for acceleration with compressed sensing (CS) due to its spatiotemporal sparsity; however, respiratory motion can degrade sparsity and lead to image artifacts. We sought to develop a motion-compensated CS method for this application.A new method, Block LOw-rank Sparsity with Motion-guidance (BLOSM), was developed to accelerate first-pass cardiac MRI, even in the presence of respiratory motion. This method divides the images into regions, tracks the regions through time, and applies matrix low-rank sparsity to the tracked regions. BLOSM was evaluated using computer simulations and first-pass cardiac datasets from human subjects. Using rate-4 undersampling, BLOSM was compared with other CS methods such as k-t SLR that uses matrix low-rank sparsity applied to the whole image dataset, with and without motion tracking, and to k-t FOCUSS with motion estimation and compensation that uses spatial and temporal-frequency sparsity.BLOSM was qualitatively shown to reduce respiratory artifact compared with other methods. Quantitatively, using root mean squared error and the structural similarity index, BLOSM was superior to other methods.BLOSM, which exploits regional low-rank structure and uses region tracking for motion compensation, provides improved image quality for CS-accelerated first-pass cardiac MRI.