Drug repositioning (DR) is a strategy to find new targets for existing drugs, which plays an important role in reducing the costs, time, and risk of traditional drug development. Recently, the matrix factorization approach has been widely used in the field of DR prediction. Nevertheless, there are still two challenges: 1) Learning ability deficiencies, the model cannot accurately predict more potential associations. 2) Easy to fall into a bad local optimal solution, the model tends to get a suboptimal result. In this study, we propose a self-paced non-negative matrix tri-factorization (SPLNMTF) model, which integrates three types of different biological data from patients, genes, and drugs into a heterogeneous network through non-negative matrix tri-factorization, thereby learning more information to improve the learning ability of the model. In the meantime, the SPLNMTF model sequentially includes samples into training from easy (high-quality) to complex (low-quality) in the soft weighting way, which effectively alleviates falling into a bad local optimal solution to improve the prediction performance of the model. The experimental results on two real datasets of ovarian cancer and acute myeloid leukemia (AML) show that SPLNMTF outperforms the other eight state-of-the-art models and gets better prediction performance in drug repositioning. The data and source code are available at: https://github.com/qi0906/SPLNMTF.