Sparse recovery space-time adaptive processing requires the use of dictionaries composed of redundant basis vectors, but sometimes the dictionary division is inaccurate. At this time, the off network effect will occur..Therefore, this paper studies the elimination of off-grid effect by two-dimensional iterative adaptive dictionary correction algorithm. In this method, the covariance matrix of clutter plus noise is estimated by the 2D IAA-STAP algorithm, and then the atoms most relevant to clutter points are obtained. The maximum joint likelihood function is used to search the clutter Doppler frequency atoms in the local area. Finally, a new space-time oriented dictionary is formed by iteration. The experimental simulation shows that the proposed method can make the clutter points attach to the clutter ridge better and reduce the off-grid effect more effectively.