Climate extremes can severely impact socio-economic development. Climate trends of three temperature and three precipitation climate indices were evaluated in observational data, 23 models from the 5th Coupled Model Intercomparison Projects (CMIP5), and 20 models from CMIP6. The climate indices were calculated over the whole of China, and individually over the basins of its three major rivers. The indices are the spatio-temporal evolution characteristics of annual mean temperature (Tas), minimum of daily minimum temperature (TNn), maximum of daily maximum temperature (TXx), number of tropical nights (TR), daily precipitation (Pre), very heavy precipitation days (R20mm), maximum consecutive 5-day precipitation (Rx5day) and consecutive dry days (CDD). From 1961 to 2018, most of China has warmed; Tas, TNn, TXx and TR over China has increased by 1.7 °C, 2.8 °C, 1.1 °C and 9 days, respectively. Changes of Tas, TNn and TXx over the Yellow River Basin, Yangtze River Basin and Pearl River Basin were generally similar in sign. The most significant increase of TR was seen over the Pearl River Basin. Historical Tas was well reproduced by both CMIP5 and CMIP6 over the study regions, but obvious uncertainties exist in the simulation of Pre. In general, CMIP6 models were improved from CMIP5 models. Climate projections were calculated for the 2021–2100 period. Future warming over China would be stronger with higher SSP scenarios; TNn over China would warm seven times more under the SSP5-8.5 scenario (5.6 °C) compared to the SSP1-2.6 scenario. Future wetting over China would be stronger with higher the SSP scenarios; Under the SSP5-8.5 scenario, Pre, R20mm, Rx5day would increase by 28%, 150%, and 38%, respectively. Projected changes of CDD different by region—decreasing over most of China and the Yellow River Basin, but increasing over the Yangtze and Pearl River Basins. The higher of the emission scenario, the less significant the reduction of CDD over the two basins. This suggests that the temporal distribution of precipitation over China will become more uneven in the future, especially under the higher SSP scenarios.