Dam breaks can lead to important economic and human losses. Design floods, which are useful to assess possible dam breaks, are usually estimated through statistical analysis of rainfall and streamflow observed data. However, such available samples are commonly limited and, consequently, high uncertainties are associated with the design flood estimates. In addition, climate change is expected to increase the frequency and magnitude of extreme rainfall and flood events in the future. Therefore, a methodology based on a stochastic rainfall generator is proposed to assess hydrological dam safety by considering climate change. We selected the Eugui Dam on the Arga river in the north of Spain as a case study that has a spillway operated by gates with a maximum capacity of 270 m3/s. The stochastic rainfall generator STORAGE is used to simulate long time series of 15-min precipitation in both current and future climate conditions. Precipitation projections of 12 climate modeling chains, related to the usual three 30-year periods (2011-2024; 2041-2070 and 2071-2100) and two emission scenarios of AR5 (RCP 4.5 and 8.5), are used to consider climate change in the STORAGE model. The simulated precipitation time series are transformed into runoff time series by using the continuous COSMO4SUB hydrological model, supplying continuous 15-min runoff time series as output. Annual maximum flood hydrographs are selected and considered as inflows to the Eugui Reservoir. The Volume Evaluation Method is applied to simulate the operation of the Eugui Dam spillway gates, obtaining maximum water levels in the reservoir and outflow hydrographs. The results show that the peak outflows at the Eugui Dam will be lower in the future. Therefore, maximum reservoir water levels will not increase in the future. The methodology proposed could allow practitioners and dam managers to check the hydrological dam safety requirements, accounting for climate change.