One of the cruxes of the three-dimensional (3D) eddy current finite element methods (FEM) is to solve large finite element equations economically. In this paper a 3-D eddy-current FEM using a four component formulation of complete variables to study skewed rotor induction motors is described. An iterative process among the four components during the solution of large algebraic equations is presented in this paper. The proposed method overcomes the nonconvergence problems if the ICCG method or the shifting ICCG method is used directly. The algorithm also requires much less computer storage compared with the Gaussian elimination method.