With the increasing complexity of the power grid and the concerns on major blackouts, there is an urgent need for an efficient and effective tool to assess the power system structural vulnerability. To tackle this challenge, this paper proposes a maximum flow-based complex network approach to identify the critical lines in a system. The proposed method consists of two major steps. First, the power network is modeled as a graph with edges (transmission lines, transformers, etc.) and nodes (buses, substations, etc.). The critical scenarios are identified by using the principal component analysis and convex hull. Then the second step is to use an improved maximum flow-based complex network approach for topology analysis. Weighted vertices in the network are considered, enabling taking the selected operating conditions into consideration when identifying the vulnerable lines. The proposed method is validated using the western Danish power system. The vulnerable lines in the network are ranked. Simulation results demonstrate the effectiveness of the method by intentional attacks and comparison with the planning strategy from the system operator.