Figuring out the convergence and persistence of per capita CO2 emissions matters much for environmental policy makers in both developed and developing countries. The Kyoto Protocol aims at avoiding threat from climate warming for human beings. CO2 emissions have been viewed as the main cause of climate change in recent decades. Thus, loads of empirical studies contribute to investigate the convergence of per capita CO2 emissions by implementing various econometric models including as many sample countries as possible. By applying a battery of univariate unit root tests, quantile unit root test, and a newly developed quantile unit root test with Fourier function, we re-investigate the convergence, mean-reverting properties and asymmetric behavior of per capita CO2 emissions in 21 OECD countries. The findings show that per capita CO2 emissions of Austria, Finland, Japan, Netherlands, New Zealand, Norway, Sweden, Switzerland and the US perform converging as a whole from the perspective of the FQKS statistics. Besides, mean-reverting properties are identified for Austria, Finland, Japan, Netherlands, Norway, Sweden, Switzerland and the US when economy is in recession. Finally, asymmetric behaviors of per capita CO2 emissions are detected at selected quantiles. All of the results provide impressive environmental economic implications for policy makers.