Changes in rainfall and streamflow due to climate change have an adverse impact on hydropower generation reliability and scheduling of cascade hydropower stations. To estimate the impact of climate change on hydropower, a combination of climate, hydrological, and hydropower scheduling models is needed. Here, we take the Jinsha River as an example to estimate the impact of climate change on total power generation of the cascade hydropower stations and residual load variance of the power grid. These two goals are solved by applying an improved multi-objective cuckoo search algorithm, and a variety of strategies for the optimal dispatch of hydropower stations are adopted to improve the efficiency of the algorithm. Using streamflow prediction results of CMIP5 climate data, in conjunction with the Xinanjiang model, the estimated results for the next 30 years were obtained. The results indicated that the negative correlation between total power generation and residual load variance under the RCP 2.6 scenario was weaker than that under the RCP 8.5. Moreover, the average power generation and the average residual load variance in RCP 2.6 was significantly larger than that in RCP 8.5. Thus, reducing carbon emissions is not only beneficial to ecological sustainability, but also has a positive impact on hydropower generation. Our approaches are also applicable for cascade reservoirs in other river catchments worldwide to estimate impact of climate change on hydropower development.