Water supply system aims to meet the user’s demand by securing water resources in a stable way. However, water supply failure sometimes happens because inflow decreases during drought period. Droughts induced by the lack of precipitation do not always lead to water supply failures. Thus, it is necessary to consider features of actual water shortage event when we evaluate a water supply risk. In this study, we developed a new drought index for drought management, i.e., Joint Drought Management Index (JDMI), using two water supply system performance indices such as reliability and vulnerability. Future data that were estimated from GCMs according to RCP 4.5 and 8.5 scenarios were used to estimate future water supply risk. After dividing the future period into three parts, the risk of water supply failure in the Nakdong River basin was analyzed using the JDMI. As a result, the risk was higher with the RCP 4.5 than the RCP 8.5. In case of RCP 4.5, W18 (Namgangdam) was identified as the most vulnerable area, whereas in case of RCP 8.5, W23 (Hyeongsangang) and W33 (Nakdonggangnamhae) were identified as the most vulnerable area.