Abstract: An iterative block DL (i.e. Davidson-Lanczos) algorithm is presented for computing a few of the largest (or lowest) eigenvalues and corresponding eigenvectors of very large sparse symmetric matrices. It's convergence rate is also discussed. it overcomes the disadvantages of the DL method which cann't find multiple or clustered eigenvalues, and the convergence speed of the mesent method is far faster than the DL method. Numerical results are compared whith those by the DL algorithm in a few experiments which exhibit a sharp-superiority of the new approach.