This paper studies the market efficiency and relevant issues of the copper futures traded on the Shanghai Futures Exchange (SHFE) in China. Since its listing, the market, grown unceasingly in scale and internationalization level, has become the largest copper futures trading market in the world (the London Metal Exchange (LME) copper futures market is the second largest). Using the data from 2006 to 2022 as a sample, a period covering the outbreak of the COVID-19 pandemic and the internationalization of the Chinese copper futures, this paper analyzes the market efficiency of China’s copper futures based on both intertemporal and intermarket strategies (SHFE Copper Futures and LME Copper Futures, with considering time difference factor). To better reflect the actual situation, this paper, when establishing trading strategy models, not only took into account various actual trading factors such as transaction costs, market impact costs, liquidity costs, margin, and capital costs but also combined daily and high-frequency data to present highly practical arbitrage strategies. According to empirical results, overall, it was not found significant arbitrage opportunities to violate the market efficiency rule. Although some arbitrage opportunities indeed emerged, they were infrequent, especially when transaction costs were considered. Specifically, in terms of the intertemporal strategy, despite that infrequent arbitrage opportunities did appear in the SHFE copper futures market, they failed to bring substantial gains, some of which even caused losses in extreme cases. In terms of the intermarket strategy, there is a cointegration relationship between the logarithmic price of LME copper futures and the logarithmic price of SHFE copper futures. The average annualized rates of return in the results of the in-sample empirical analysis were high, but in the out-of-sample empirical analysis of high frequency and daily data were not found significant arbitrage opportunities. The influence between the LME copper futures market and the SHFE copper futures market was bidirectional.