Single-cell RNA sequencing (scRNA-seq) measures expression profiles at the single-cell level, which sheds light on revealing the heterogeneity and functional diversity among cell populations. The vast majority of current algorithms identify cell types by directly clustering transcriptional profiles, which ignore indirect relations among cells, resulting in an undesirable performance on cell type discovery and trajectory inference. Therefore, there is a critical need for inferring cell types and trajectories by exploiting the interactions among cells. In this study, we propose a network-based structural learning nonnegative matrix factorization algorithm (aka SLNMF) for the identification of cell types in scRNA-seq, which is transformed into a constrained optimization problem. SLNMF first constructs the similarity network for cells and then extracts latent features of the cells by exploiting the topological structure of the cell-cell network. To improve the clustering performance, the structural constraint is imposed on the model to learn the latent features of cells by preserving the structural information of the networks, thereby significantly improving the performance of algorithms. Finally, we track the trajectory of cells by exploring the relationships among cell types. Fourteen scRNA-seq datasets are adopted to validate the performance of algorithms with the number of single cells varying from 49 to 26,484. The experimental results demonstrate that SLNMF significantly outperforms fifteen state-of-the-art methods with 15.32% improvement in terms of accuracy, and it accurately identifies the trajectories of cells. The proposed model and methods provide an effective strategy to analyze scRNA-seq data. (The software is coded using matlab, and is freely available for academic https://github.com/xkmaxidian/SLNMF).