Recognizing changes in the supply–demand relationship of Flood Regulation Service (FRS) is significant for the rational planning of urban patterns and the prevention of flooding risks in river basins. Most existing studies have explored its spatial pattern but pay less attention to its spatiotemporal changes. This study explored the dynamic changes in the supply–demand relationship of FRS in rapidly urbanizing basins. We proposed the Supply-Demand Ratio (SDR) method, which used the Soil Conservation Service Curve Number (SCS-CN) model and the flood vulnerability index to quantify the supply and demand of FRS, and then, we calculated the SDR. Additionally, we calculated the rate of change in SDR from 1990 to 2018 in the basin and its subbasins. The case study in the Baiyangdian Lake Basin showed that the SDR method can effectively measure the changes in the relationship between the supply and demand of FRS in the river basin. The SDR was consistent with the supply–demand bivariate mapping method, with Kappa coefficients of 0.610 and 0.835 in 1990 and in 2018, respectively. Furthermore, we found that from 1990 to 2018, the imbalance of FRS in supply and demand intensified. The SDR for the whole basin decreased by 0.088 from 1990 to 2018, with a change rate of −27.8%. Rapid urbanization is an important reason for intensification of the FRS supply–demand imbalance. The proportion of urban area is the most relevant factor for the supply–demand relationship of FRS, with a Pearson correlation coefficient of −0.845 (p < 0.01). Therefore, we suggest that proactive policies be adopted to defend against flood disaster risks in the future construction of the Xiong'an New Area, which is located downstream from the Baiyangdian Lake Basin.