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Achieving carbon neutrality before 2060 newly announced in China are expected to substantially affect air quality. Here we project the pollutants emissions in China based on a carbon neutrality roadmap and clean air policies evolution; national and regional PM2.5 and O3 concentrations in 2030 (the target year of carbon peak), 2035 (the target year of "Beautiful China 2035" launched by the Chinese government to fundamentally improve air quality) and 2060 (the target year of carbon neutrality) are then simulated using an air quality model. Results showed that compared with 2019, emissions of SO2, NOx, primary PM2.5, and VOCs are projected to reduce by 42%, 42%, 44%, and 28% in 2030, by 57%, 58%, 60%, and 42% in 2035, by 93%, 93%, 90% and 61% in 2060 respectively. Consequently, in 2030, 2035, and 2060, the national annual mean PM2.5 will be 27, 23, and 11 μg m-3; and the 90th percentile of daily 8-h maxima of O3 (O3-8h 90th) will be 129, 123, and 93 μg m-3; 82%, 94%, and 100% of 337 municipal cities will reach the current national air quality standard, respectively. It's expected that the "Beautiful China 2035" target is very likely to be achieved, and about half of the 337 cities will meet the current WHO air quality guideline in 2060. In the near future, strict environmental policies driven by "Beautiful China 2035" are needed due to their substantial contribution to emission reductions. By 2060, the low-carbon policies driven by the carbon neutrality target are expected to contribute to larger than 80% of reductions in PM2.5 and O3-8h 90th concentrations relative to the 2020 levels, implying that more attention could be paid to low-carbon policies after 2035. Our research would provide implications for future co-governance of air pollution and climate change mitigation in China and other developing countries.