This paper investigates the multi-dimensional risk spillover effects of carbon markets with energy, non-energy commodity and stock markets in China before and after the COVID-19 outbreak, through the DY network with GARCHSK-VaR method. The empirical results denote that the total bidirectional risk spillovers of carbon markets become larger after the COVID-19 outbreak than before the COVID-19 outbreak. Interestingly, in both periods, energy is the largest risk contributor to carbon markets, while carbon markets become the net risk contributors to stock markets under COVID-19. Furthermore, compared with Guangdong pilot, the impacts of Hubei pilot on other markets are stronger in both periods. Finally, the dynamic risk spillover effects have obvious differences between before and after the COVID-19 outbreak.