Abstract: Focusing on the performance degradation of sparse recovery space-time adaptive processing (SR-STAP) due to the presence of off-grid, a local search orthogonal matching pursuit algorithm is proposed. In the proposed algorithm, the global grid point which is matched with clutter is first selected from the global STAP overcomplete dictionary. Then the local STAP overcomplete dictionary is designed, whose center is the above selected global grid point and the size of which is the spatial and temporal frequency intervals. By selecting the local grid point which is matched with the clutter ridge from the local STAP dictionary, the angleDoppler profile of clutter and the modified STAP dictionary are obtained. Simulation results demonstrate that, the proposed algorithms can select the grid point more matched with the clutter ridge, and significantly improve the performance of SR-STAP.