Abstract: A quasi-direct solution (QDS) for the finite difference equations has been developed, which is basel on the sparse and pivot-dominant properties of the matrix and is the combination of the direct method and the iterative method. The principle and the features of QDS method have been discussed. A comparison has been made with the successive over-relaxation (SOR) method. It is shown that the QDS method requires less computer memory than the direct method, covnerges faster than the SOR method and is suitable for calculating the finite difference equations of electromagnetic and magnetostatic problems.