Abstract The partial charge-simulation method is presented to solve the characteristic impedance of transmission line of specific cross-section with offset inner conductors. This method has a higher accuracy due to the accurate satisfaction of the boundary condition on the outer conductor. The combined method of gnass elimination and optimization is used to solve the equation of charge-simulation, and it is an effective method for increasing the accuracy and assuring the convergence. The Green's functions of five transmission lines (i.e.with circular, elliptic, rectangular, trough and slab outer conductor) are given.