The development of 3D Synthetic Aperture Radar (SAR) imaging is currently hampered by issues such as high data dimension, high system complexity, and low imaging processing efficiency. Sparse SAR imaging has grown in importance as a research branch in SAR imaging due to the high potential of sparse signal processing techniques based on Compressed Sensing (CS) to show high potential in reducing system complexity and improving imaging quality. However, traditional sparse imaging methods are still constrained by high computational complexity, nontrivial parameter tuning, and poor adaptability to weakly sparse scenes. To address these issues, we propose a new 3D SAR imaging method based on learned sparse priors inspired by the deep unfolding concept. First, the limitations of the matrix-vector linear representation model are discussed, and an imaging operator is introduced to improve the algorithm’s imaging efficiency. Furthermore, this research focuses on algorithm network details, such as network topology design, the problem of complex-valued propagations, optimization constraints of algorithm parameters, and network training details. Finally, through simulations and measured experiments, it is proved that the proposed method can improve the imaging accuracy while reducing the running time by more than one order of magnitude compared with the conventional sparse imaging algorithms.