The evaluation of vulnerable nodes in complex distribution networks is becoming more and more difficult. In order to effectively establish the quantitative relationship among the levels of the evaluation indicators, a membership function of grade division is proposed to describe the vulnerability characteristics among the levels of the evaluation indicators. Firstly, according to the topological structure of the distribution network and the actual operating conditions, four indexes, namely node series, active power degree and voltage increment severity based on load impact and fault breaking, were proposed to analyze the entire distribution network. Based on the discrete degree of index changes, entropy weight method was adopted to determine the weight of each index. Then, a membership function is used to establish a membership model for each index of vulnerable nodes. Finally, the weak links in the distribution network are identified by calculating the vulnerability value of each node of the distribution network through membership matrix algorithm. The calculation results show that the proposed comprehensive vulnerability evaluation system is in line with the actual situation, effectively identify the vulnerable nodes in the distribution network, and verifies the rationality and practicability of the system.