Abstract: A method is proposed to suppress reverberation in the deep sea. Assuming the characteristics of low-rank for sidelobe and sparsity for mainlobe of signal in the tempo-spatial domain, the problem of reverberation suppression is formulated as a matrix decomposition of low-rank matrix, sparse matrix, and turbulence matrix. The low-rank matrix is achieved by using the algorithm of the Grassmann manifold, and the sparse matrix is obtained with the constraint of sparsity for the sparse matrix. The effectiveness of the proposed method is verified by a simulation with the random orthogonal model and the random sparsity model. Further, the performance of the proposed method is validated via data, which consists of deep-sea reverberation obtained from the experiment in the South China Sea and the simulated target echo. It is demonstrated that the time consumption of the proposed method is reduced by 55% compared to the method of SRPSS, for a similar detection performance.