The development of human society and the production and operation activities of enterprises have brought about global warming, resulting in frequent natural disasters. It has become the consensus of all countries in the world to develop a green and low-carbon economy. Under this background, enterprises, as the main body of economic activities, especially energy industry enterprises, should optimize and upgrade the traditional production and operation mode with high pollution, high consumption, and low output to a high-efficiency and low-pollution mode, and pay attention to the co-ordinated development of economic benefits, social benefits, and ecological benefits. Financial performance evaluation indicators have become the main basis for senior leaders of energy industry enterprises to make decisions and evaluate the low-carbon economic benefits of enterprises. This paper constructs a set of financial evaluation index systems of energy industry enterprises under the background of a low-carbon economy from four dimensions: profitability, asset quality, debt risk, and business growth. The analytic hierarchy process (AHP) is used to measure the comprehensive contribution of financial indicators of low-carbon production and operation. The purpose of this study is to provide scientific financial management decisions for energy enterprises to reduce costs and increase the efficiency and low-carbon operation under the background of a low-carbon economy. The research results show that the comprehensive evaluation index system after the traditional financial evaluation index of energy industry enterprises is integrated with the evaluation index of a low-carbon economy can help enterprises make more correct and effective financial decisions in the process of survival, development, and growth, and, at the same time, the financial evaluation index of a low-carbon economy should pay more attention to the indicators with a higher comprehensive contribution, so as to effectively promote the low-carbon operation efficiency of enterprise production, management, and sales. Compared with other research results, this paper innovatively constructs a financial management decision-making index system for measuring the low-carbon operation of energy enterprises in theory, which has important value in guiding energy enterprises to reduce costs and increase the efficiency and low-carbon operation in practice.