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With the frequent occurrence of extreme weather events in the world, the ability of power system to resist disasters has attracted more attention. In this paper, a method to evaluate the resilience of distribution networks by focusing on the impact of critical loads under extreme weather events is proposed, and typhoon is taken as the representative to formulate a vulnerability curve of components. Furthermore, the Monte Carlo method is used to simulate the whole process of extreme weather disaster and to generate the fault scenario. Different weights are assigned to different levels of load according to the importance of load, and the weighted loss of load is selected as the evaluation index of resilience. Finally, the method is verified by the IEEE-33 bus system. The results demonstrate that this method is effective to quantify the resilience of distribution networks under extreme weather events.