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An approximate analytical scheme is proposed in this paper to evaluate the integration of the Green's function, on the background of parallel interconnects. The free-space Green's function is expanded in Taylor's series and integrated term-wise. Instead of handling double-volume integrals directly by numerical or purely analytical means, the expressions of double-line integrals for two parallel filaments are first derived. Following the clue to geometrical mean distance, for the expanded terms of nonnegative orders, a second-order mean distance is introduced to represent the role of the cross section so that the volume integration can be evaluated by using the formulas of line integration. Numerical results show that the presented method bears better performance than existing approaches.