This article proposes novel sparsity-aware space-time adaptive processing (SA-STAP) algorithms with \(l_1\)-norm regularization for airborne phased-array radar applications. The proposed SA-STAP algorithms suppose that a number of samples of the full-rank STAP data cube are not meaningful for processing and the optimal full-rank STAP filter weight vector is sparse, or nearly sparse. The core idea of the proposed method is imposing a sparse regularization (\(l_1\)-norm type) to the minimum variance (MV) STAP cost function. Under some reasonable assumptions, we firstly propose a \(l_1\)-based sample matrix inversion (SMI) to compute the optimal filter weight vector. However, it is impractical due to its matrix inversion, which requires a high computational cost when in a large phased-array antenna. Then, we devise lower complexity algorithms based on conjugate gradient (CG) techniques. A computational complexity comparison with the existing algorithms and an analysis of the proposed algorithms are conducted. Simulation results with both simulated and the Mountain Top data demonstrate that fast signal-to-interference-plus-noise-ratio (SINR) convergence and good performance of the proposed algorithms are achieved.