Cell type identification is a crucial step towards the study of cellular heterogeneity and biological processes. Advances in single-cell sequencing technology have enabled the development of a variety of clustering methods for cell type identification. However, most of existing methods are designed for clustering single omic data such as single-cell RNA-sequencing (scRNA-seq) data. The accumulation of single-cell multi-omics data provides a great opportunity to integrate different omics data for cell clustering, but also raise new computational challenges for existing methods. How to integrate multi-omics data and leverage their consensus and complementary information to improve the accuracy of cell clustering still remains a challenge. In this study, we propose a new deep multi-level information fusion framework, named scMIC, for clustering single-cell multi-omics data. Our model can integrate the attribute information of cells and the potential structural relationship among cells from local and global levels, and reduce redundant information between different omics from cell and feature levels, leading to more discriminative representations. Moreover, the proposed multiple collaborative supervised clustering strategy is able to guide the learning process of the core encoding part by learning the high-confidence target distribution, which facilitates the interaction between the clustering part and the representation learning part, as well as the information exchange between omics, and finally obtain more robust clustering results. Experiments on seven single-cell multi-omics datasets show the superiority of scMIC over existing state-of-the-art methods.