Abstract: Sparse recovery（SR） space time adaptive processing（STAP） could suppress clutter using a small number of clutter samples， but it highly relies on the space time dictionary. When there was a yaw angel between the direction of the aircraft crab and the antenna placement， the clutter would deviate from the dictionary grids， what we called off-grid. It would cause the degradation of clutter suppression. In this paper， as the reason of some sparse recovery off-grid algorithms don’t performance well when there exists noise and they don’t use the sparsity of clutter well. We proposed a l_p norm based STAP algorithm. Firstly， a dynamic dictionary SR STAP model is built. Then the model is relaxed to a l_p norm nonconvex problem. Finally， the problem is transformed to a weighted l₁ norm problem， and a two-step iterative method is proposed to find the solution. Numerical results show proposed algorithm can recover the clutter accurately， and has better performance in clutter suppression than the variational inference based algorithm.