Assessment of climate change impacts on regional hydrological processes is vital for effective water resource management and planning. The 2015 Paris Agreement includes a two-headed temperature goal: “holding the increase in the global average temperature to well below 2 °C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 °C”. The current study assesses the potential effect of global warming of 1.5 °C and 2 °C on river discharge, and their differences in the Upper Yangtze River Basin (UYRB) based on three hydrological models (HBV, SWAT and VIC) driven by bias-corrected climate projections from five General Circulation models (GCMs), namely GFDL, HAD, IPSL, MIROC and NOR as abbreviated, and two Representative Concentration Pathways (RCP2.6 and RCP4.5). Results indicate that all discharges (except autumn) especially winter have slight decreasing tendency (−0.3%, −2.3%, −0.8%, −6.4%, −1.2%, −0.3% respectively for annual, spring, summer, winter, 90% percentile and 10% percentile discharges) under RCP2.6 during 2020–2039 (+1.5 °C global warming) comparing to the reference period of 1986–2005. However, all discharges (except autumn and winter) especially summer have an increasing tendency (1.1%, 1.1%, 3.7%, 0.9%, 2.1% respectively for annual, spring, summer, 90% percentile and 10% percentile discharges) under RCP4.5 during 2040–2059 (+2 °C global warming). Moreover, the occurrence frequency and strength of droughts in dry season under global warming of 1.5 °C will increase, while floods in wet season under global warming of 2 °C tend to increase in UYRB. Additionally, the difference of river discharge between global warming of 2 °C and 1.5 °C is positive for almost all the time scales (1.4%, 3.5%, 4.5%, 2.1%, 2.4% respectively for annual, spring, summer, 90% percentile and 10% percentile discharges), which suggests that the increment of 0.5 °C could lead to more flood events in the UYRB.