The cross-border congestion management method with maximizing transmission capability value is effective， which can be used to calculate congestion costs on the cross-border interconnection lines. However， how to appropriately allocate congestion costs remains unsolved. A new method based on liability is proposed to allocate the congestion costs among consumers and providers by electrical dissection method. Each marketing participator pays for the congestion costs in proportion to its liability. Simulation results on an improved IEEE 30 nodes system indicate the correctness and effectiveness of the proposed method.