In the context of dual carbon targets and the launch of the national carbon market, power producers need to make trading decisions in both the electricity and carbon markets. At present, relevant research has not deeply considered the medium and long-term electricity market and the speculative behavior of power producers in the carbon market. To this end, this paper proposes a joint decision-making model for power producers to participate in the carbon market and the mid- and long-term electricity market. The model takes the one-year carbon market compliance period as the optimization period, and on the basis of considering the speculative behavior of power producers, uses the conditional value at risk to describe the profit risk caused by market price uncertainty. At the same time, the model improves the deficiency that the carbon price in the carbon market is only assumed to be a fixed value, and overcomes the problem that the carbon quota constraint originally based on the compliance period is forcibly decomposed into each trading period in the electricity market. This paper conducts case studies based on relevant market data in Guangdong Province, and compares the proposed decision-making model with the traditional one. The results show that power producers can make decisions based on the model in this paper considering the electricity market and carbon market, and can obtain better comprehensive benefits. This work is supported by the Key Project of National Natural Science Foundation of China (No. 51937005).