The COVID-19 epidemic has severely affected the world economy and energy markets. In order to alleviate the shock, stabilize the financial market, and promote economic recovery, the Fed announced an unlimited QE policy. In order to understand the impact of the policy on the energy market under the extreme events, the study selected WTI crude oil and coal prices from January 1, 2018 to May 7, 2021 as the research objects. Taking the two years before the epidemic, the epidemic stage was further divided into four small stages according to the three peaks of the epidemic in the US. The MF-DCCA model calculations show that coal and WTI crude oil have an interactive relationship. The risks between them are not just averaged and superimposed, but transmitted and interacted.The MF-DFA model calculation results show that due to the disorder of energy supply and demand under the epidemic, market efficiency in the first quarter of 2020 has dropped rapidly. However, market efficiency decoupled from the development of the epidemic in the second half of 2020. Especially after the announcement of the QE policy, market efficiency has improved significantly. However, under the excessive monetary policy, market efficiency declined in the first half of 2021. This shows that the policy has a certain effect on alleviating the impact of the epidemic on the energy market. But this improvement is not sustainable from the long term. As prices rise, inflation continues. In the future, the volatility and risk of the energy futures market will increase. Display omitted •The efficiency of the energy market declined during the epidemic.•Second half of 2020 has the largest increase in market efficiency.•The coal market is less efficient than the WTI crude oil market in the first half of 2021.•Risk transmission between coal and WTI crude oil markets.•The effectiveness of QE policies in alleviating energy market turmoil is gradually weakening.