The relative performance of global climate models (GCMs) of phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6, respectively) was assessed in this study based on their ability to simulate annual and seasonal mean rainfall and temperature over Bangladesh for the period 1977–2005. The multiple statistical metrics were used to measure the performance of the GCMs at 30 meteorological observation stations. Two robust multi-criteria decision analysis methods were used to integrate the results obtained using different metrics for an unbiased ranking of the GCMs. The results revealed MIROC5 as the most skilful among CMIP5 GCMs and ACCESS-CM2 among CMIP6 GCMs. Overall, a significant improvement in CMIP6 MME compared to CMIP5 MME was noticed in simulating rainfall over Bangladesh at annual and seasonal scales. CMIP6 MME also showed significant reduction in maximum and minimum temperature biases over Bangladesh. However, systematic wet and cold biases still exist in CMIP6 models for Bangladesh. CMIP6 GCMs showed higher spatial correlation with observed data compared to CMIP5 GCMs, but higher difference in terms of standard deviations and centered root mean square errors, indicating better performance in simulating geographical distribution but lower performance in simulating spatial variability of most of the climate variables for different timescales. In terms of Taylor skill score, the CMIP6 MME showed higher performance in simulating rainfall but lower performance in simulating temperature compared to CMIP5 MME for most of the timeframes. The findings of this study suggest that the added value of rainfall and temperature simulations in CMIP6 models is incompatible with the climate models used in this research.