Faced the vast amount of information, choosing the appropriate materials is a prerequisite for effective self-directed learning. The recommendation algorithm is a kind of intelligent technology that can accurately locate the required information which the users care about most. However, many recommendation techniques experience can not be trained adequately in scenarios with small sample data and extremely sparse ratings. Moreover, DLRAs (Deep learning based Recommendation Algorithms) require high hardware support. The probabilistic graph (PG) can effectively represent the implicit complex relations among nodes, but it still has the problem of sparse data sensitivity. Therefore, we propose a Matrix-Factorization-based Probabilistic Graph Model for Recommendation Algorithm (MF-PGMRA): By matrix-factorizing the sparse rating matrix, the users and items are mapped to the user/item spaces, respectively; We employ the inner product to data-enhance and overcome the problems of sparse data and cold start; Then, we build Probabilistic Graph to construct the "user-item" latent spaces and estimate the probability distribution based on expectation maximization (EM), so as to predict the ratings; Finally, we built a library management system with the recommendation module to highlight the benefits of MF-PGMRA for students' subject learning. According to a questionnaire, we confirmed that the students are satisfied with the system from four aspects of speed, accuracy, usability and convenience, which can confirm that the library management system based on MF-PGMRA can efficiently and accurately recommend suitable materials for students from the huge amount of learning materials to improve students' self-directed learning efficiency.