With the increase in the proportion of photovoltaic and wind power access, the scale and form of distribution networks are becoming more and more complex. The traditional single distribution network vulnerability assessment method is difficult to use to identify the vulnerable links in the distribution network. Therefore, this paper proposes a method for identifying and evaluating vulnerable links in distribution networks based on minimum discriminant information. First, considering the influence of distributed grid connection, an improved probabilistic power flow calculation method is proposed, which improves the calculation efficiency and accuracy. Second, considering the correlation degree, transmission capacity, and voltage stability of branches in the distribution network, the identification index of vulnerable lines is defined. Based on power quality and operating state, the identification index of vulnerable nodes in a distribution network is defined. Finally, based on the indicators of vulnerable nodes and vulnerable lines, the vulnerable links in the distribution network are comprehensively evaluated based on the principle of minimum discriminant information, and the vulnerable links of the entire distribution network are evaluated according to different degrees of vulnerability. The rationality and effectiveness of the proposed method are verified via an example analysis of actual power grid data.