Four-dimensional (4D) MRI can provide 3D tissue properties and the temporal profiles at the same time. However, further applications of 4D MRI is limited by the long acquisition time and motion artifacts. We propose a new 4D MRI reconstruction scheme, named HDTV-LLR, by integrating the three-dimensional higher degree total variation and the local low-rank penalties. We demonstrate the benefits of the proposed method using 4D cardiac MRI dataset with undersampling factors of 12 and 16. The proposed method is compared with iGRASP, and schemes using either low-rank or sparsity constraint alone. Results show improved image quality and reduced artifacts.