To enhancing a small fraction of critical components in the face to extreme disturbances can effectively improve the power grid resilience. In this paper, identifying the set of vulnerable components in the power system that most affect its resilience is investigated. First, based on the resilience process curve, the largest amount of power supply of a given topology was proposed to quantify power grid resilience, which was calculated with the optimal power flow model and simplex method. Then, a multi-objective optimization model was built, and two indicators, the number of damaged components and the maximum power that the grid can provide, were used as objective functions. Second, three intelligent optimization algorithms were selected to solve the established multi-objective optimization model. Simulation results show that the proposed method can effectively identify the critical components that have a significant impact on power system resilience, compared with commonly used methods.