Low carbon economy emphasizes innovative, green, and high-quality economic growth mode. The deep integration and coordinated development of the industry chain, innovation chain and service chain are an effective measure and inevitable requirement to transform the pattern of economic growth and boost the low-carbon economy. Taking the data of Wuhan, Nanchang and Changsha, the central cities of the middle reaches of the Yangtze River city cluster, from 2013 to 2020 as samples, this paper discusses the mechanism of the three-chain coordinated development to promote high-quality economic development, uses the coupling coordination model to measure the three-chain coordination degree, and the grey relational degree model to predict the future development of the three chains in this region. The research results show that: since the establishment of the case city cluster, the three chains of the central cities have experienced a change from disharmony to gradual coordinated development, and the trend is good. However, the coordination degree is still low at present, which is not conducive to the sustainable development of regional economy. According to the research results, policy suggestions are put forward to promote intra-city three-chain coordination and inter-city three-chain integration coordination.