The application of iterative soft threshold (IST) algorithm for dynamic magnetic resonance imaging (MRI) image reconstruction based on low-rank and sparse matrix decomposition exists two problems of the poor reconstruction accuracy and conver ge speed.Considering these problems,total variation (TV) regularization based on low-rank and sparse matrix decomposition model is introduced to further remove noise and artifacts.Besides, inexact augmented Lagrangian method (IALM) is used for fast reconstruction.In order to verify the effectiveness of the proposed method,the simulations about reconstruc tion of cardiac perfusion MRI and cardiac cine MRI are done.The results of the simulation demonstrate that: using IALM for low-rank and sparse matrix decomposition reconstruction results in better reconstruction performance than using IST method.Although introducing TV regularization reduces the reconstruction speed compared with IALM,it still fast than IST,and the recon struction accuracy is higher than that of IALM.So introducing TV regularization to the low-rank a nd sparse matrix decomposition model can improve the MRI reconstruction accuracy,and using IALM a lgorithm can speed up the reconstruction speed.The combination of TV regularization and IALM algor ithm has achieved the purpose of rapid and high precision reconstruction.