The compressed-sensing-based methods use the global or the local sparse dictionaries separately, which respectively results in the loss of image details or overall structures of MR(magnetic resonance) images. In order to solve this problem, a novel imaging algorithm combining both local and global sparse constraints was proposed to capture details and overall structures of MR images. Firstly, a spare dictionary was trained from specific MR images, and then the local sparse representations were obtained via the dictionary. Secondly, traditional analytical dictionaries were used to promote the global sparse structures of MR images. Finally, the reconstruction was solved by using a nonlinear conjugate gradient with the known local and global sparse constraints. This procedure was repeated iteratively to improve the quality of reconstruction. And experimental results demonstrate that compared with the dictionary learning magnetic resonance imaging method (dictionary learning MRI, DLMRI), the proposed algorithm can improve the image reconstruction by 1-6 dB when the reduction factor is up to 10.