This study evaluates the performance of 12 different general circulation models (GCMs) from the Coupled Model Intercomparison Project Phase 5 (CMIP5) to simulate precipitation and temperature in the Koshi River Basin, Nepal. Four statistical performance indicators: correlation coefficient, normalised root-mean-square deviation (NMRSD), absolute NMRSD, and average absolute relative deviation are considered to evaluate the GCMs using historical observations. Seven different climate indices: consecutive dry days, consecutive wet days, cold spell duration index, warm spell duration index, frost days, very wet days, and simple daily intensity index are considered to identify the most suitable models for the basin and future climate impact assessment studies. Weights for each performance indicator are determined using the entropy method, with compromise programming applied to rank the GCMs based on the Euclidian distant technique. The results suggest that CanESM2 and CSIRO-MK3.6.0 are the most suitable for predicting extreme precipitation events, and BCC-CSM 1.1, CanESM2, NorESM1-M, and CNRM-CM5 for extreme temperature events in Himalayan river basins. Overall, IPSL-CM5A-MR, CanESM2, CNRM-CM5, BCC-CSM 1.1, NorESM1-M, and CSIRO-Mk3.6.0 are deemed suitable models for predicting precipitation and temperature in the Koshi River Basin, Nepal.