To solve the problem of two non-smooth regularization terms in sparse reconstruction of Magnetic Resonance Imaging (MRI) based on Compressed Sensing (CS), a new Proximal Smoothing Iterative Algorithm (PSIA) based on Moreau-envelope was proposed. The classical sparse reconstruction for MRI based on CS is a problem of minimizing the objective function with a linear combination of three terms:the least square data fidelity term, the sparse regularization term of wavelet transform, and the Total Variation (TV) regularization term. Firstly, the proximal smoothing of the wavelet transform regularization term in the objective function was carried out. Then, the linear combination of the data fidelity term and the wavelet transform regularization term after smooth approximation was considered as a new convex function that could be continuously derived. Finally, PSIA was used to solve the new optimization problem. The proposed algorithm can not only cope with the two regularization constraints simultaneously in the optimization problem, but also avoid the algorithm robustness problem caused by fixed weights. The experimental results on simulated phantom images and real MR images show that, compared with four classical sparse reconstruction algorithms such as Conjugate Gradient (CG) decent algorithm, TV l₁ Compressed MRI (TVCMRI) algorithm, Reconstruction From Partial k space algorithm (RecPF) and Fast Composite Smoothing Algorithm (FCSA), the proposed algorithm has better reconstruction results of image signal-to-noise ratio, relative error and structural similarity index, and its algorithm complexity is comparable to the existing fastest reconstruction algorithm FCSA.