As the linkage between the crude oil market and the stock market is increasing, studying the correlation characteristics between the two markets and analyzing the impact of crude oil price fluctuations on the stock market will help avoid risks and ensure sustained and stable economic growth. The Copula-GARCH model is used to empirically analyze the return sequence of WTI crude oil price and the return sequence of NASDAQ stock index. The results show that the GARCH(1,1)-t model fits the conditional marginal distribution of the two sequences best and the time-varying SJC Copula model can better describe the correlation between the two markets than the often correlated Copula model. There is a positive correlation between the two return rate series, the correlation is time-varying, and the correlation structure has a certain asymmetry. The upper-tail correlation coefficient is smaller than the lower-tail correlation coefficient, that is, the possibility of extreme price drops in the two markets at the same time Bigger. This provides a certain reference basis for risk management in China's financial market and avoiding the impact of oil price fluctuations on the stock market.