The goal of this study is to derive water resource vulnerability characteristics for South Korea according to individual district populations in a changing climate. The definition of water resource vulnerability in this study consists of potential flood damage and potential water scarcity. To quantify these vulnerabilities, key factors, or indicators affecting vulnerability, are integrated with a technique for order of preference by similarity to ideal solution (TOPSIS), which is a multi-criteria decision-making approach to determine the optimal alternative by considering both the best and worst solutions. The weight for each indicator is determined based on both the Delphi technique and Shannon’s entropy, which are employed to reduce the uncertainty in the process of determining the weights. The Delphi technique reflects expert opinions, and Shannon’s entropy reflects the uncertainty of the performance data. Under A1B climate change scenarios, medium-sized districts (200,000–300,000 inhabitants) are the most vulnerable regarding potential flood damage; the largest districts (exceeding 500,000 inhabitants) are found to be the most vulnerable with respect to potential water scarcity. This result indicates that the local governments of cities or districts with more than 200,000 inhabitants should implement better preventative measures for water resources. In addition, the Delphi and entropy methods show the same rankings for flood vulnerability; however, these approaches produce slightly different rankings regarding water scarcity vulnerability. Therefore, it is suggested that rankings from not only subjective but also objective weights should be considered in making a final decision to implement specific adaptive measures to climate change.