Abstract: ‍ ‍The space-time adaptive processing （STAP） technology jointly performs signal processing in the time （pulse dimension） and space （array dimension） dimensions to realize the dynamic target detection function. However， the computational complexity of traditional STAP technology is substantial， and it needs the support of large samples when optimizing the signal processing. In real-world scenarios， the cluttered and changing environment complicates acquiring sufficient independent and identically distributed samples， resulting in suboptimal clutter suppression. Sparse recovery space-time adaptive processing （SR-STAP） algorithms are capable of achieving clutter suppression with a limited number of training samples. However， the majority of SR-STAP algorithms have considerable computational complexity， slow running speed， and low real-time performance. In addition， the SR-STAP algorithm needs to discretize the continuous space-time two-dimensional plane， and the space-time two-dimensional plane is divided into several small grids. The continuous distribution of real clutter across the space-time plane， coupled with noise and system parameter errors in radar signals， leads to discrepancies between actual clutter points and discretized grid points. This grid mismatch affects the clutter suppression performance of the SR-STAP algorithm. To address this issue， this paper proposes a dictionary mismatch correction SR-STAP algorithm based on local grid adaptive division. First， the algorithm selects the atoms that have the highest correlation with clutter using the subspace projection method. Subsequently， adaptive local grid division is performed around the selected atoms from coarse to fine. According to the local grid iterative optimization criterion， the optimal atoms in the local area are constantly adjusted and selected until the iteration termination condition is satisfied to match the real clutter points. Finally， the clutter subspace is constructed using the space-time steering vector corresponding to the selected optimal atom， and the STAP weight is obtained by updating the projection matrix orthogonal to the clutter subspace on the noise subspace. Simulation results show that， compared with the traditional SR-STAP algorithm， the proposed algorithm has higher sparse recovery accuracy， faster running speed， and improved STAP performance.