The electricity load surge during the decades has caused frequent transmission congestion problems, which seriously impact the safety of the power systems. In traditional congestion management mathematical models, owing to the strong non-linearity and non-convexity of the N-1 constraints, the computation burden is usually heavy especially for the large scale systems. Hence, this paper trained a deep neural network (DNN) to surrogate the N-1 constraints. Firstly, the data samples are generated based on the good-point set theory. The power generation volume and the load level were used as the input of the DNN and the violation of the N-1 constraints were considered as the training target. Then the well-trained DNN was embedded into the traditional congestion management models which were solved by genetic algorithm (GA). The proposed method was tested on the IEEE 30 system. Numerical results showed that with the comparison of the traditional congestion management method, the proposed approach achieved higher computation efficiency and accuracy.