A better understanding of variations of extreme precipitation in space and time is essential for hydro-meteorological research and effective management of water resources. We used 11 extreme precipitation indices, some additional indices, and four seasonal precipitation based on daily precipitation data from 24 meteorological stations in West Rapti River basin (WRRB) of Nepal during 1986-2015 as the baseline, and three future periods (Near Future or NF: 2025-2049, Mid Future or MF: 2050-2074, and Far Future or FF: 2075-2099). This study also attempts to correlate the streamflow at downstream station of the basin with extreme precipitation indices in the baseline period and employed the relation to estimate future streamflow. We used five climate models of the fifth phase of the Coupled Model Inter-comparison Project (CMIP5) under two representative concentration pathways (RCPs 4.5 and 8.5) to project future extreme precipitation indices. A linear scaling method of bias correction was used to reduce the biases in precipitation data of the climate models. Mann-Kendall test in conjunction with Theil-Sen's slope method was employed for trend analyses and their statistical significance. We found that extreme precipitation indices related to very wet days, extremely wet days, maximum 1-day, and maximum 5-day precipitation amounts are anticipated to increase significantly in future days. Our results showed percentage contribution of maximum 1-day, and maximum 5-day precipitation amounts to annual precipitation are important indicators of extreme precipitation. Higher percentage contributions were observed in lower regions indicating higher occurrences of very heavy precipitation in flatter topography. The increase in rainfall extremes would increase the possibility of frequent hydrological disasters in WRRB in the coming days. Generally, river valleys attain less extreme precipitation and are comparatively drier. We believe the findings of this study are useful for water resources management in WRRB under changing climate.