The large-scale interconnection of the power grid has brought great benefits to social development, but simultaneously, the frequency of large-scale fault accidents caused by extreme weather is also rocketing. The power grid is regarded as a representative complex network in this paper to analyze its functional vulnerability. First, the actual power grid topology is modeled on the basis of the complex network theory, which is transformed into a directed-weighted topology model after introducing the node voltage together with line reactance. Then, the algorithm of weighted reactance betweenness is proposed by analyzing the characteristic parameters of the power grid topology model. The product of unit reliability and topology model’s characteristic parameters under extreme weather is used as the index to measure the functional vulnerability of the power grid, which considers the extreme weather of freezing and gale and quantifies the functional vulnerability of lines under wind load, ice load, and their synergistic effects. Finally, a simulation using the IEEE-30 node system is implemented. The result shows that the proposed method can effectively measure the short-term vulnerability of power grid units under extreme weather. Meanwhile, the example analysis verifies the different effects of normal and extreme weather on the power grid and identifies the nodes and lines with high vulnerability under extreme weather, which provides theoretical support for preventing and reducing the impact of extreme weather on the power grid.