With the tremendous increase of publicly available single-cell RNA-sequencing (scRNA-seq) datasets, bioinformatics methods based on gene co-expression network are becoming efficient tools for analyzing scRNA-seq data, improving cell type prediction accuracy and in turn facilitating biological discovery. However, the current methods are mainly based on overall co-expression correlation and overlook co-expression that exists in only a subset of cells, thus fail to discover certain rare cell types and sensitive to batch effect. Here, we developed independent component analysis-based gene co-expression network inference (ICAnet) that decomposed scRNA-seq data into a series of independent gene expression components and inferred co-expression modules, which improved cell clustering and rare cell-type discovery. ICAnet showed efficient performance for cell clustering and batch integration using scRNA-seq datasets spanning multiple cells/tissues/donors/library types. It works stably on datasets produced by different library construction strategies and with different sequencing depths and cell numbers. We demonstrated the capability of ICAnet to discover rare cell types in multiple independent scRNA-seq datasets from different sources. Importantly, the identified modules activated in acute myeloid leukemia scRNA-seq datasets have the potential to serve as new diagnostic markers. Thus, ICAnet is a competitive tool for cell clustering and biological interpretations of single-cell RNA-seq data analysis.