This paper constructs the evaluation index system of Civic and Political Education and Digital Economy Development and uses the entropy value method to calculate the weight value of each index in the evaluation system. A gray correlation analysis model is established to explore the degree of correlation and relevance of indicators in the evaluation system of ideological and political education and economic development. Analyze the synergistic development between the two subsystems of ideological and political education and digital economic development by using the coupling degree and the coupling coordination degree analysis method, and explore the degree of coordination of the coupling development between the two. The analysis of the relationship between civic and political education and economic development in the sample sites found that the integrated gray correlation between the two is 0.610, which is a moderate level of correlation. The coupling degree of the two is increasing year by year, and it will reach 0.525 in 2023. On average, the coupling coordination degree reaches 0.610, which belongs to primary coordination. This paper provides data support for the improvement of the coupling coordination between ideological education and economic development in the era of the digital economy. It lays the foundation for the common development of ideological education and economy.