Innovation and entrepreneurship education teaching is an important driving force to stimulate the innovation ability of college and university students and to improve them, which puts forward a major test for the teaching ability of college and university teachers as a key part of teaching. This paper analyzes the current situation of the teaching ability of college teachers in innovative entrepreneurship education teaching through a questionnaire survey. It constructs the evaluation index system of innovation and entrepreneurship teaching ability of college teachers, combines the gray correlation analysis method to determine the weight of each index in the system, and finally successfully constructs the rating system of innovation and entrepreneurship teaching ability of college teachers. Regression analysis and gray correlation methods are used to explore the influencing factors of college teachers’ ability to teach innovation and entrepreneurship. It was found that five factors, such as school type, education, and title, had a significant impact on college teachers’ innovation and entrepreneurial teaching ability. The correlation between participation in innovation and entrepreneurship training and the innovation and entrepreneurship teaching ability of college teachers in the gray correlation calculation is 0.758, which has a significant effect on teachers’ innovation and entrepreneurship teaching ability.