Clutter background suppression is a critical problem in synthetic aperture radar-ground moving target indication (SAR-GMTI). In general, a great quantity of secondary data is not easily acquired in heterogeneous environments. To solve the problem of clutter suppression, a method based on nonlocal self-similarity-robust principal component analysis (NSS-RPCA) is proposed for airborne SAR systems. First, discrete clutter is separated from the echo data by RPCA after range pulse compression. Second, similar blocks of the residual-clutter background are extracted to overcome the training sample limitation using the NSS method in the 2-D time domain. Third, subcovariance matrices are structured by the similar blocks, and the subcovariance matrix is stacked into a tensor. Then, the subclutter covariance matrix can be obtained from the stacked subcovariance matrix tensor by RPCA, where the residual-clutter tensor is of low rank and the target tensor is sparse. Finally, the residual clutter can be suppressed by the subclutter covariance matrix. In this manner, the source of independent identically distributed (IID) samples will be increased significantly without aperture loss by the proposed method. Simulation and analysis based on the experimental data illustrate the effectiveness of the proposed method.