Urban flooding introduces significant risk to society. Non-stationarity leads to increased uncertainty and this is challenging to include in actual decision-making. The primary objective of this study was to develop a risk assessment and decision support framework for pluvial urban flood risk under non-stationary conditions using an influence diagram (ID) which is a Bayesian network (BN) extended with decision and utility nodes. Non-stationarity is considered to be the influence of climate change where extreme precipitation patterns change over time. The overall risk is quantified in monetary terms expressed as expected annual damage. The network is dynamic in as much as it assesses risk at different points in time. The framework provides means for decision-makers to assess how different decisions on flood adaptation affect the risk now and in the future. The result from the ID was extended with a cost-benefit analysis defining the net benefits for the investment plans. We tested our framework in a case study where the risk for flooding was assessed on a railway track in Risskov, Aarhus. Drainage system improvements are planned for the area. Our study illustrates with the use of an ID how risk for flooding increases over time, and the benefits of implementing flood adaptation measures.