The problem of climate change caused by excessive energy consumption has attracted worldwide attention to economic development patterns. Based on China's GDP, fossil energy and other energy consumption data from 1998 to 2018, this paper studies the relationship between China's economic growth and energy consumption by establishing an econometric model. The results of the co-integration equation show that there is a stable long-term equilibrium relationship between the consumption of oil, natural gas and other energy resources and economic growth, and that natural gas consumption has a significant impact on China's economic growth. Every 1% increase in GDP will lead to 9.0436% increase in natural gas consumption. Granger causality test shows that economic growth is the cause of energy consumption growth, but the increase of energy consumption is not the cause of economic growth. The error correction model shows that in the short term energy consumption is adjusting to the long-term equilibrium very quickly. Finally, based on the empirical results, some countermeasures and Suggestions are put forward to maintain China's economic development and reduce its dependence on fossil energy.