Direction Of Arrival(DOA) study has always been focused on the accuracy and the computational complexity. While the existing algorithms, which are based on the compressive sensing theory, have advantages over the traditional, there are still problems with high computational complexity and low estimation accuracy because the signal model is on the equal spacing grid. To solve those problems, a partially refined grid method is proposed. The proposed method consists of fission process and learning process, the fission process is to refine angle space by inserting new grid points, the learning process is constantly approaching the direction of arrival. The proposed algorithm takes less time and has higher accuracy under sparse initial grid(the initial interval is 20°).