Since the global financial crisis in 2008, international energy markets have become more closely linked to financial markets and energy prices have exhibited more financial characteristics. Therefore, it is of great theoretical and practical significance to study the time-varying synergy between the energy market and the global financial market. This paper sets up a model for realizing the time-varying co-movements between energy markets and global financial markets: It uses the Diebold &Yilmaz spillover index method and its dynamic expansion model to test the spillover mechanism of market volatility shocks, applies the deep long and short-term memory (DLSTM) model to predict market prices. The results of this study show that, first, energy markets and global financial markets are closely linked networks, and the spillover effects have obvious time-varying characteristics. Second, from a static spillover perspective, the Global Financial Price Index shows the largest net exporter in both yield and volatility spillovers, suggesting that the global financial development market has the strongest influence on other markets. However, in the volatility spillover, the net spillover index shows alternating periods of positive and negative periods most of the time.