The emergence of sparse reconstruction methods for undersampled data in Magnetic Resonance Imaging (MRI), such as Compressed Sensing (CS), have been valuable tools to accelerate data acquisition while preserving accurate image reconstruction. However, sparse reconstruction methods, including CS, are not easy to apply when there is intra-frame motion. Such is the case of free-breathing dynamic MRI in the liver. It is difficult to avoid non-rigid motion artifacts, even more so in volumetric acquisitions. To avoid these kind of artifacts, we propose a new reconstruction technique tailored for dynamic liver imaging by estimating the motion between frames to correct inconsistencies in k-space measurements. In this work, we describe how the proposed method addresses an increase in image efficiency for free-breathing dynamic 3D liver MRI, producing gains up to 6 dB with respect of traditional CS framework. Our technique can be readily extended to 3D CINE liver MRI without requiring additional information.