Congestion problems of transmission lines are very important research issues in power system operations. Load curtailment is one of the ways to solve congestion problems by a major contingency. A systematic and effective mechanism for load shedding has been developed by investigating congestion distribution factors and the direct load control program. In this paper, a load shedding algorithm using linear programming for congestion problems by a major contingency is presented. In order to show the effectiveness of the proposed algorithm, it has been tested on the 6-bus sample system and the power system of Korea, and their results are presented.