Symmetry is important for differential-transmission lines, but the dense parallel traces easily break the symmetry due to coupling with the adjacent conductor, leading to mode conversion. We propose an asymmetric geometry of differential-transmission lines placed on the side of a nonadjacent conductor to suppress mode conversion and maintain signal integrity in the cases of loosely coupled and tightly coupled parallel traces. By designing the asymmetric geometry of dense differential-transmission lines by taking into account coupling with the adjacent conductor, mode conversion was successfully suppressed by decreasing the line width on the side of the non-adjacent conductor. It was also found that the asymmetric geometry can suppress mode conversion and maintain signal integrity in tightly coupled parallel traces. In loosely coupled parallel traces, on the other hand, the tightly coupled asymmetrically tapered bend we previously proposed suppresses mode conversion.