The computer information service industry is closely related to the fourth industrial revolution and stands at the core of the global value chain. It has become an essential engine for developing industries in various countries, and its scale is constantly expanding. In the critical period of global economic transformation and development, the use of mathematical models to predict its international competitiveness will help scientifically evaluate the development level of the industry and accelerate the adaptation to the needs of the fourth industrial revolution. In this article, a prediction model is proposed for the international competitiveness of the computer information service industry. First, we used the Revealed Comparative Advantage (RCA) index to measure the international competitiveness of the computer information service industry. Furthermore, based on the characteristics of the industry and high-quality development theory, we constructed the evaluation indicator system of influencing factors and used the grey relational analysis method to screen key indicators. Then, we combined the Grey model and BP neural network algorithm to construct the GM-BP prediction model. Finally, China is used as an example to predict the international competitiveness of its computer information service industry, and suggestions are made for industrial development. The results show that the grey relational analysis method can genuinely reflect the impact of different aspects on the international competitiveness of China’s computer information service industry and better determine the key indicators of influencing factors. The GM-BP model has minor errors and excellent simulation results and can accurately predict the future status of international competitiveness. The applicability and reliability of the model are reasonable.