A model-by-model analysis for historical simulations was necessary for identifying reasonably performing models in the updated Coupled Model Intercomparison Project (CMIP6) over the Tibetan Plateau. To determine whether the capacity of the CMIP6 models in simulating temperature and precipitation over the Plateau has been enhanced, we compared the outputs of 23 CMIP6 models with an observational dataset (CN05.1) for the period 1961–2014. The results suggest the systematic model biases (cold bias and wet bias) in the Tibetan Plateau still exist in CMIP6. Most models in CMIP6 realistically simulated the surface temperature and spatial distribution of precipitation, with a pattern correlation exceeding 0.75. The bias in the mean surface temperature of the multi-model ensemble (MME) simulation was 1.08 °C lower than the observational data, which had been decreased compared with the cold bias of CMIP5 (1.52 °C). At the seasonal scale, most models exhibited a warm temperature bias in summer and a cold bias in winter. The CMIP6 MME displayed a higher reproducibility of the precipitation amplitude over dry regions compared with CMIP5 and a lower ability over wet regions.