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When an extreme weather event occurs, the temporary closure of airports is inevitable. In this case, airlines need to optimize their flight schedules in short order to reduce losses. However, it is very hard to address a large-scale disruption within a short time using traditional methods. In this paper, FVNS, a fast variable neighborhood search-based algorithm, is proposed to solve this problem. The method can be divided into two stages. The first stage is the construction stage, i.e., postponing the affected flights and constructing a feasible flight plan. The second stage is the improvement stage. In this stage, by searching for and implementing cost-effective flight swap operations, the flight plan is improved, and the optimal flight plan is finally obtained. The results of the test examples show that both the computational results and the computational speed are significantly better than those of the previous methods. Linear programming and local search are the two main algorithms used in flight recovery research. In this paper, we compare and analyze the advantages and disadvantages of each algorithm with examples and note that researchers should develop local search algorithms to form a practical general algorithm framework.