The quality of dynamic magnetic resonance imaging reconstruction has heavy impact on clinical diagnosis. In this paper, we propose a new reconstructive algorithm based on the L + S model. In the algorithm, the l1 norm is substituted by the lp norm to approximate the l0 norm; thus the accuracy of the solution is improved. We apply an alternate iteration method to solve the resulting problem of the proposed method. Experiments on nine data sets show that the proposed algorithm can effectively reconstruct dynamic magnetic resonance images.