Abstract: The Sparse Recovery Space-Time Adaptive Processing (SR-STAP) method can use a small number of training range cells to effectively suppress the clutter of airborne radar. The SR-STAP approach may successfully eliminate airborne radar clutter using a limited number of training range cells. However, present SR-STAP approaches are all model-driven, limiting their practical applicability due to parameter adjustment difficulties and high computational cost. To address these problems, this study, for the first time, introduces the Deep Unfolding/Unrolling (DU) method to airborne radar clutter reduction and target recognition by merging the model-driven SR method and the data-driven deep learning method. Firstly, a combined estimation model for clutter space-time spectrum and Array Error (AE) parameters is established and solved using the Alternating Direction Method of Multipliers (ADMM) algorithm. Secondly, the ADMM algorithm is unfolded to a deep neural network, named AE-ADMM-Net, to optimize all iteration parameters using a complete training dataset. Finally, the training range cell data is processed by the trained AE-ADMM-Net, jointly estimating the clutter space-time spectrum and the radar AE parameters efficiently and accurately. Simulation results show that the proposed DU-STAP method can achieve higher clutter suppression performance with lower computational cost compared to typical SR-STAP methods.