The existing literature mainly documents the relationship between international and domestic fossil energy markets; however, empirical evidence of the dynamic relationships between fossil energy market and new energy market is lacking. This paper combines TGARCH model and copula model to explore the dynamic linkages and spillover effects between international fossil energy (crude oil, coal and natural gas) markets and China's new energy market using daily data from 4 January 2012 to 3 September 2018. The empirical results indicate that fossil energy returns and new energy returns are positive related over time. And the crude oil returns and new energy returns, as well as the coal returns and new energy returns have lower tail dependence, while there is upper tail dependence structure between natural gas returns and new energy returns. Furthermore, the extreme upside and downside risk spillover from international fossil energy markets to China's new energy market is asymmetric. Among the spillover effects, the downward risk spillover of crude oil market exerts the most significant impact on China's new energy market.