The invention relates to a non-convex low-rank reconstruction method for rapid MR imaging. An MR image data reconstruction mathematic model based on low-rank prior information of non-local similar image blocks is established, and iterative solution is carried out on the model in a direction alternative iteration method; a non-convex p norm of the low-rank matrix of the non-local image model with the low-rank prior information is solved by deposition and iteration of Taylor first-order approximation and the singular value, a similar image block is obtained, and a reconstruction image is solved via iteration by increasing the auxiliary variable and separating the variable. The image prior information is used to combine the non-local similarity with the low-rank characteristic of the image block, the Fourier transform and the characteristic of the low-rank matrix are used to simplify the calculation process, the complexity of algorithm is reduced, the performance of the reconstructed MRI images by part of K space data is improved, the image can be reconstructed more accurately with less scanning and measurement, pseudo shadows of the images are reduced, and rapid MRI is realized.