Matrix factorization in collaborative filtering recommendation algorithms is widely used because of its simplicity and facility of implementation, but matrix factorization utilizes a simple linear inner product to model the non-linear interaction between the user and the item, which limits the model's expressive power. He et al. proposed a generalized matrix factorization model, which extended the matrix factorization to the generalized matrix factorization through a non-linear activation function and connection weights, and gave the model the ability to model second-order non-linear interactions between users and items. Nevertheless, the generalized matrix factorization model is a shallow model and does not model the high-order interaction between users and items, which may affect the performance of the model to a certain extent. Inspired by the generalized matrix factorization model, this study proposes a deep matrix factorization model, abbreviated as DMF. Based on the generalized matrix factorization model, a hidden layer is introduced, and a deep neural network is used to learn the higher-order interaction between users and items. The deep matrix factorization model, which has a good expression ability, not only solves the linear problem of simple inner product, but also models high-order interactions between users and items. In addition, a lot of rich comparative experiments are performed on two datasets, MovieLens and Anime, and the results confirm its feasibility and effectiveness. Meanwhile the optimal parameters of the model were determined through experiments.