Currently the explainable recommendation systems (RS) have been developed for indicating the reasons why a product is recommended to the user and illustrating the correlation between the user’s preferences and the product. One of the state-of-the-art methods in RS is latent model based on matrix factorization and its variations. This study proposes an Explainable Biased Matrix Factorization (EBMF) model. This model takes into account both bias and the quantification of explainability of the users and items which are employed in the matrix factorization model. Specifically, the bias compensates the user-item’s interaction and the quantification of explainability is known as the explainability score of recommended item for specific user. To investigate the effects of the proposed EBMF model, we make a comparison of the performance of EBMF model with those of various baseline models, including Matrix factorization, Explainable matrix factorization, Global average rating, User average rating and Item average rating on different datasets. Experimental results show that the proposed EBMF model can improve the prediction performance compared to other approaches.