The depths of snow in the Qinghai-Tibetan Plateau simulated by 19 phase five of the Coupled Model Inter-Comparison Project (CMIP5) models are assessed in comparison with the observation ones from passive microwave satellite remote-sensing (PMSR) and 72 weather stations. The annual regional mean snow depths (ARMSDs) from 1851 to 2005 indicate decreases for most of the models but slight increases for CMCC-CM, FGOALS-g2, and CanESM2. The simulated ARMSD anomalies vary from -10 cm to 20 cm, and the amplitudes exhibit obvious decreases over the recent 50 years. In the period from 1986 to 2005, the spatial distributions of the annual mean snow depth (AMSD) simulated by MRI-CGCM3, CCSM4, CESM1-BGC, CESM1-CAM5, and CESM1-WACCM are quite similar to those from the PMSR observations. But the maximum and mean AMSD values simulated by all 19 models are much larger than those observed by PMSR. The inter-annual variation of snow, which occurs primarily in the Middle and East Tibetan Plateau, is simulated relatively well by inmcm4. From 1960 to 2005, the ARMSDs simulated by most of the models show decreases but are increasing according to actual observations. Only five models produce positive trends that agree with the observations. According to the selected indices, the CCSM4, MIROC5, MRI-CGCM3, and FGOALS-g2 models are selected as relatively good models for predicting the plateau snow, and the 21st century changes in the snow climate in the Qinghai-Tibetan Plateau are projected using these four models.