For multichannel airborne radars, wide-area groundmoving target indication (WGMTI) processing can quickly obtain the dynamic distribution of moving targets in a wide area, which holds considerable significance in many fields. Nevertheless, the WGMTI mode suffers from the interference of powerful ground clutter, which frequently submerges slow-moving targets and causes many false alarms in subsequent moving target detection. Space-time adaptive processing (STAP) can successfully suppress clutter, but its performance depends critically on the available training samples. Consequently, an effective STAP method characterized by fast processing and a small sample size for WGMTI application in multichannel airborne radars must be developed. In this paper, a subarray-level sparse recovery STAP (SR-STAP) processing framework is proposed for multichannel airborne radars. First, the characteristics of the subarray-level received clutter are discussed in detail. Second, on the basis of this analysis, we further designed a joint space-time dictionary and developed a separable tensor-based sparse Bayesian learning (STSBL) method.