With the rapid development of the economy and the transformation of social contradictions, the economic development model in China has also changed, and a high-quality economic development model has been proposed. This paper uses the entropy method to measure the level of innovation and high-quality economic development in nine prefecture-level cities in Fujian Province from 2011 to 2020, and finds that the overall level shows an increasing trend year by year, but there are obvious regional differences. By constructing a grey correlation degree model, it is found that the innovation subsystem and the high-quality economic development are strongly correlated, the development level of innovation and the subsystem of high-quality economic development are both strongly correlated, the grey correlation degree from high to low is green, coordinated, shared, and livelihood, indicating that innovation has a significant impact on high-quality economic development. Based on the research results, countermeasures and suggestions are proposed to promote the coordinated development of innovation and high-quality economy.