Due to human-induced global warming, global Average Surface Air Temperature(ASAT) will reach certain thresholds with reference to the pre-industrial period. Quantitative assessments of climate extremes across China when reaching these thresholds are important indicators in disaster risk management and policymaking. In this study, based on outputs of 18 General Circulation Models(GCMs) from the Coupled Model Intercomparison Project Phase 5(CMIP5), 27 climate-extreme indices computed with a consistent methodology are used to quantify the changes in the mean and extreme climate across China when the 2℃, 3℃, and 4℃ thresholds under different Representative Concentration Pathways(RCP) scenarios are exceeded. In general, the ASAT warms faster over China than the global mean in the 21st century. Extreme warm events(e.g., warm nights, warm days, and tropical nights) increase greatly, while extreme cold events(e.g., cold nights, cold days, and frost days) decrease. When the 4℃ threshold is exceeded, warm nights index(spatially averaged over China) are projected to show an increase of about 49.9% relative to the reference period. Accompanied by the increase in global mean temperature, the northern part of China will see more precipitation when the 2℃ threshold is exceeded. Extreme precipitation shows obvious intensification in both frequency and magnitude when different temperature thresholds are exceeded. China is dominated by lengthening heavy and very heavy precipitation days and increasing maximum consecutive 5-day precipitation and extremely wet days. Under the RCP8.5 scenario, the maximum consecutive 5-day precipitation amount increases by 12.5mmand 17.0mmwhen the global ASAT becomes 3℃ and 4℃ warmer, respectively. The changes are found to be more pronounced under higher temperature thresholds. Southwest China, however, exhibits larger changes in the magnitude of extreme precipitation than other regions.