The ADI method is considered here for a class of unsymmetric linear systems Ax = b arising from the non-self-adjoint elliptic partial differential Eq. . If the matrix A is split into parts H and V, i.e., A = H + V then we consider the case where H and V have complex spectra. The convergence and optimum parameter determination of the ADI method with one and two parameters are studied. First it is shown that the ADI method with one parameter r converges for any positive r and the optimum parameter r can be given analytically. Then it is shown that the optimum ADI method with two parameters is better than the one parameter ADI method in most cases. A procedure for determining the two optimum parameters is given. The numerical comparisons between the ADI method with one and two parameters are included.