Abstract: For conventional Space-Time Adaptive Processing (STAP), sufficient Independent and Identically Distributed (IID) samples are hard to obtain by the clutter within heterogeneity. To mitigate this problem, a Compressive Sensing (CS) based Ground Moving Target Indication (GMTI) method is proposed. In the method, firstly the space-time data of the interested range bin are transformed to two-dimensional frequency fields to accumulate the signal energy and the corresponding redundant dictionary is constructed; Then several primary clutter spectrum peaks are extracted by Bayesian compressive sensing technique to estimate the clutter ridge; Finally, the weighted l1 minimization optimization model is constructed to realize the ground moving target indication. Simulation results and theory analysis demonstrate that the proposed method attains good resolution meanwhile it takes on excellent performance in low SNR.