Passive multiple sound source localization is a challenging problem in underwater acoustics, especially for a short hydrophone array in the deep ocean. Several attempts have been made to solve this problem by applying compressive sensing (CS) techniques. In this study, one greedy algorithm in CS theory combined with a spatial filter was developed and applied to a two-source localization scenario in the deep ocean. This method facilitates localization by utilizing the greedy algorithm with a spatial filter at several iterative loops. The simulated and experimental data suggest that the proposed method provides a certain localization performance improvement over the use of the Bartlett processor and the greedy algorithm without a spatial filter. Additionally, the effects on the source localization caused by factors such as the array aperture, number of hydrophones or snapshots, and signal-to-noise ratio (SNR) are demonstrated.