In this paper, a new direction-of-arrival (DOA) estimation method is proposed based on the array cross-correlation vector (ACCV) model which can decrease the computational complexity of multiple measurement vectors (MMV) model. Firstly, the ACCV model is refined to accommodate the correlated signal scenario. Then by properly incorporating the folding scheme in the compressive sensing (CS) framework, a new algorithm termed folding orthogona matching pursuit (FOMP) is proposed in the reconstruction of CS framework. The method has a lower computational complexity and higher performance compared with other existing DOA algorithms. Numerical results are presented to verify the efficiency of the proposed method.