Experiential teaching is based on modern teaching approaches, including the construction of knowledge, the generation of emotion, and the development of ability through students’ personal experiences. Compared with traditional teaching, it has characteristics of autonomy, practice, and interaction. This is conducive to promote students’ autonomous learning, speeding up the transfer of knowledge and experience, and improving students’ personal comprehensive ability. There are various forms of experiential teaching methods in management teaching, but they should be selected reasonably according to the teaching contents. In the actual application of experiential teaching, teachers should carefully design teaching plans, pay attention to comments and summaries, and ensure the unity of theoretical teaching and experiential learning. This research work investigates experiential teaching based on modern teaching concepts and explores three application mechanisms of the experiential teaching method in the first stage. In the second stage, it proposes an algorithm to evaluate the promotion of experiential education based on modern teaching concepts in college management. The proposed algorithm is named improved gray wolf optimization-Back Propagation (IGWO-BP). IGWO balances the full search and the local search through a nonlinear convergence factor and makes the leadership gray wolf dynamically guide the population forward through a variable proportional weight. Then, IGWO is used to optimize the BP network to improve evaluation accuracy and convergence speed. Compared with the state-of-the-art machine learning methods, the proposed mechanism achieves the highest accuracy of 94.6% and an F1 score of 91.3%.