An alternating minimization method for the reconstruction of MR images with wavelet sparsity，including the convergence analysis of this algorithm，is presented in this paper.Our algorithm is base on a half-quadratic penalty method.The optimization problem with wavelet sparsity is splited into two sub-problems:the X-subproblem and the Y-subproblem.The solution for the original problem can be obtained by alternately solving the two subproblems，in which the Y-subproblem is solved via a 1D soft-thresholding or shrinkage and the X-subproblem is solved by a Fourier transform approach.Thus，the splitting algorithm for solving the original problem is generated.The phantom image and some real MR images are employed to test our approach in the numerical experiments.The alternating minimization algorithm is also compared to the state-of-the-art algorithm，operator splitting algorithm.The experimental results demonstrate that the alternating minimization algorithm has not only a greater signal-to-noise ratio(SNR)，but has also less relative errors and is faster than the operator splitting algorithm.Therefore the alternating minimization method is a fast reconstruction method for sparse MR images.