Advancements in single-cell technologies concomitantly develop the epigenomic and transcriptomic profiles at the cell levels, providing opportunities to explore the potential biological mechanisms. Even though significant efforts have been dedicated to them, it remains challenging for the integration analysis of multi-omic data of single-cell because of the heterogeneity, complicated coupling and interpretability of data. To handle these issues, we propose a novel self-representation Learning-based Multi-omics data Integrative Clustering algorithm (sLMIC) for the integration of single-cell epigenomic profiles (DNA methylation or scATAC-seq) and transcriptomic (scRNA-seq), which the consistent and specific features of cells are explicitly extracted facilitating the cell clustering. Specifically, sLMIC constructs a graph for each type of single-cell data, thereby transforming omics data into multi-layer networks, which effectively removes heterogeneity of omic data. Then, sLMIC employs the low-rank and exclusivity constraints to separate the self-representation of cells into two parts, i.e., the shared and specific features, which explicitly characterize the consistency and diversity of omic data, providing an effective strategy to model the structure of cell types. Feature extraction and cell clustering are jointly formulated as an overall objective function, where latent features of data are obtained under the guidance of cell clustering. The extensive experimental results on 13 multi-omics datasets of single-cell from diverse organisms and tissues indicate that sLMIC observably exceeds the advanced algorithms regarding various measurements.