The traditional Direction of Arrival (DOA) estimation algorithms require a large amount of sampling data, which causes high computational complexity. To address this problem, based on the compressive sensing theory, a beamspace based Regularized Multi-vector Focal Undetermined System Solver (RMFOCUSS) DOA estimation algorithm is proposed, which uses the spatial sparsity characteristic of targets of interest.The proposed algorithm maps the received compressed signals from the element-space to the beamspace, which overcomes the flaw that the sparse reconstruction algorithm cannot be used under the conditions of low SNR to some extent. Numerical simulations demonstrate that:1) Compared with the traditional CaponMUSIC and l1-SVD algorithms, the proposed algorithm can effectively carry out DOA estimation of the coherent signals with higher angle resolution and estimation accuracy;and 2) Compared with the element-space based RMFOCUSS and l1-SVD algorithms, the proposed method has a lower computational complexity.