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We present a new multilevel matrix compression method (MLMCM) and its application to the analysis of scattering problems from three-dimensional (3-D) arbitrary-shaped conductors. The compression is achieved without generating the full subblocks of the matrix by the rank-based method. Unlike the conventional rank-based method, incoming compression matrix and outgoing compression matrix are defined when coupling with a cluster of its far interaction groups. Only a small translation matrix is redefined for every two coupling groups. The merits of the proposed method are: 1) it is kernel function-independent and can be applied to arbitrary complex media; 2) it is more efficient than conventional rank-based methods. This paper shows numerical results to demonstrate the validity of the proposed method.