The near-range clutter of airborne nonside-looking array greatly depends on range. Conventional phased-array space-time adaptive processing (STAP) radar suffers severe performance degradation in the presence of a near-range clutter scenario. To efficiently suppress no-stationary clutter with only one snapshot, an STAP algorithm for airborne multiple-input multiple-output (MIMO) radar with nonside-looking array based on sparse representation is first presented, which is referred to as MIMOSR-STAP in this paper. By exploiting the waveform diversity of MIMO radar, each snapshot of a tested range-cell is transformed into the multisnapshots of phased array radar, which are used to estimate the high-resolution space-time spectrum with multiple measurement vectors technique. The proposed approach is effective in estimating the spectrum by utilizing temporally correlated multiple sparse Bayesian learning. In the sequel, the clutter covariance matrix and corresponding adaptive weight vector are efficiently obtained. MIMOSR-STAP enjoys high accuracy and robustness so that it achieves better performance of output signal-to-clutter-plus-noise-ratio and minimum detectable velocity than the single measurement vector sparse representation methods in the literature. Thus, MIMOSR-STAP performs well in a serious nonstationary clutter scenario and is suitable for an insufficient independent and identically distributed samples environment.