Respiratory motion is one of the most challenging problems in thoracic and abdominal MRI. Motion resolved reconstruction is introduced to reduce the respiratory motion effects by grouping the data to different motion states, then using compressed sensing techniques to reconstruct different motion states images. Spatio-temporal low-rank constrained reconstruction is one of the widely used techniques. In this work, we proposed a new method incorporating motion compensation into the low-rank model, called MoCoLoR. The proposed method is applied to high resolution free breathing lung MRI, and the results show that MoCoLoR outperforms the standard low-rank constrained reconstruction.