Abstract: Constructing a regularization optimization model to introduce prior information into image restoration tasks, it was a main method to solve the sparse imaging problem of synthetic aperture radar (SAR) based on compressed sensing (CS) theory. Due to the simple regularization constraints causing structural information unable provided into the complex target and with non-sparse scenes especially, a novel two-dimensional (2D) sparse SAR learning imaging method was proposed based on the plug-and-play (PnP) framework and deep unfolding networks (DUN). Firstly, an approximate observation model was derived with the chirp-scaling algorithm (CSA) to reduce computational cost. Then the sparse imaging problem was arranged to be solved iteratively based on the matched filter approximate message passing (MFAMP) method. To overcome the limitations of prior models in existing sparse imaging methods, a Plug-and-play (PnP) was introduced in the sparse reconstruction framework to replace the traditional L1 norm sparse regularization apparatus. Finally, the imaging process was unfolded to a DUN named the PnP framework and MFAMP-based SAR learning imaging network (PnP-MFAMP-Net). The experimental results show the robustness and superiority of the proposed imaging method.