Liver dynamic contrast enhanced MRI (DCE-MRI) requires high spatiotemporal resolution to clearly visualize enhancement patterns. Image reconstruction quality is often compromised due to unavoidable respiratory motion during the long-time acquisition. This abstract presents a novel sliding motion corrected low-rank plus sparse (SMC-LS) reconstruction algorithm for free-breathing liver DCE-MRI. The sliding motion of the liver along the superior-inferior direction is estimated directly from the under-sampled k-space data. Low-rank and sparse regularization are enforced on the sliding motion corrected image reconstructions. Results demonstrated that SMC-LS can substantially reduce motion blurring and preserve more details in free breathing liver DCE-MRI.