The combined effects of global warming and population growth induce policymakers to enhance flood risk management practices in order to reduce substantially the causes of floods and to mitigate their future and multiple impacts simultaneously. This way, this paper puts forward a new multi-attribute and non-stationary decision model for managing flood risks in urban areas under climate demographic changes, which we call the Non-Stationary Multi-Attribute Utility Theory (NSMAUT). Under expected utilities, our model inserts time-dependency into the decision-maker's (DM's) preference statements based on his/her trade-offs regarding psychological distance induced by delayed prospects. The NSMAUT analyzes flood risks under five attributes, linked to environmental, financial, human, mobility, and social concerns of society. By combining climate and demographic scenarios for this century, our findings make use of statistical, graphic, and risk performance measures that increase the DM's perception of risk in order to control and monitor the dynamism of circumstances of risk and thus to facilitate on what he/she should base future decisions on adapting cities for future adverse events arising from flooding. A numerical application in a Brazilian municipality from 2021 – 2100 is used to validate our approach. Moreover, the model can be replicated in other urban contexts.