This paper proposes using the sparse-recovery (SR) based 2-D multiple-signal classification (MUSIC) to enhance the multi-target detection capability of high-frequency surface wave radars (HFSWRs). Usually, for wide-beam HFSWRs, target detection is first conducted in the range-Doppler spectrum; bearings are then estimated by super-resolution methods, such as MUSIC. Unfortunately, this approach can easily result in unfavorable deterioration of multi-target detection by conventional cascaded methods if target signals tend to mix in the Doppler spectrum. To compensate this shortage, spatial-temporal joint estimation is used. Owing to the lack of spatial-temporal snapshots caused by the non-stationarity of target signals, the efficiency of the estimator is improved by multiple-measurement-vector-based sparse recovery, which has been used to solve many under-sampling problems in the past ten years. As a result, 2D SR-MUSIC improves multi-target detection and outperforms conventional cascaded methods. The results obtained using real data with opportune targets validate our approach. Multiple adjacent targets are detected and distinguished from one another.