Recent advances in biochemistry and single-cell RNA sequencing (scRNA-seq) have allowed us to monitor the biological systems at the single-cell resolution. However, the low capture of mRNA material within individual cells often leads to inaccurate quantification of genetic material. Consequently, a significant amount of expression values are reported as missing, which are often referred to as dropouts. To overcome this challenge, we develop a novel imputation method, named single-cell Imputation via Subspace Regression (scISR), that can reliably recover the dropout values of scRNA-seq data. The scISR method first uses a hypothesis-testing technique to identify zero-valued entries that are most likely affected by dropout events and then estimates the dropout values using a subspace regression model. Our comprehensive evaluation using 25 publicly available scRNA-seq datasets and various simulation scenarios against five state-of-the-art methods demonstrates that scISR is better than other imputation methods in recovering scRNA-seq expression profiles via imputation. scISR consistently improves the quality of cluster analysis regardless of dropout rates, normalization techniques, and quantification schemes. The source code of scISR can be found on GitHub at https://github.com/duct317/scISR.