The advent of single-cell RNA sequencing (scRNA-seq) techniques opens up new opportunities for studying the cell-specific changes in the transcriptomic data. An important research problem related with scRNA-seq data analysis is to identify cell subpopulations with distinct functions. However, the expression profiles of individual cells are usually measured over tens of thousands of genes, and it remains a difficult problem to effectively cluster the cells based on the high-dimensional profiles. An additional challenge of performing the analysis is that, the scRNA-seq data are often noisy and sometimes extremely sparse due to technical limitations and sampling deficiencies. In this paper, we propose a biclustering-based framework called DivBiclust that effectively identifies the cell subpopulations based on the high-dimensional noisy scRNA-seq data. Compared with nine state-of-the-art methods, DivBiclust excels in identifying cell subpopulations with high accuracy as evidenced by our experiments on ten real scRNA-seq datasets with different size and diverse dropout rates. The supplemental materials of DivBiclust, including the source codes, data, and a supplementary document, are available at https://www.github.com/Qiong-Fang/DivBiclust.