Space-time adaptive processing (STAP) algorithms based on sparse recovery (SR) have been researched because of their low requirement of training snapshots. However, once some portion of clutter is not located on the grids, i.e., off-grid problems, the performances of most SR-STAP algorithms degrade significantly. Reducing the grid interval can mitigate off-grid effects, but brings strong column coherence of the dictionary, heavy computational load, and heavy storage load. A sparse Bayesian learning approach is proposed to mitigate the off-grid effects in the paper. The algorithm employs an efficient sequential addition and deletion of dictionary atoms to estimate the clutter subspace, which means that strong column coherence has no effect on the performance of the proposed algorithm. Besides, the proposed algorithm does not require much computational load and storage load. Off-grid effects can be mitigated with the proposed algorithm when the grid-interval is sufficiently small. The excellent performance of the novel algorithm is demonstrated on the simulated data.