Transmission congestion management plays a key role in deregulated energy markets. To correctly model and solve this problem, power system voltage and transient stability limits should be considered to avoid obtaining a vulnerable power system with low stability margins. Congestion management is modeled as a multi-objective optimization problem in this paper. The proposed scheme includes the cost of congestion management, voltage stability margin and transient stability margin as its multiple competing objectives. Moreover, a new effective Multi-objective Mathematical Programming (MMP) solution approach based on normalized normal constraint (NNC) method is presented to solve the multi-objective optimization problem of the congestion management, which can generate a well-distributed and efficient Pareto frontier. The proposed congestion management model and MMP solution approach are implemented on the New-England's test system and the obtained results are compared with the results of several other congestion management methods. These comparisons verify the superiority of the proposed approach. (C) 2015 Elsevier Ltd. All rights reserved.