We develop a method, VIPER, to impute the zero values in single-cell RNA sequencing studies to facilitate accurate transcriptome quantification at the single-cell level. VIPER is based on nonnegative sparse regression models and is capable of progressively inferring a sparse set of local neighborhood cells that are most predictive of the expression levels of the cell of interest for imputation. A key feature of our method is its ability to preserve gene expression variability across cells after imputation. We illustrate the advantages of our method through several well-designed real data-based analytical experiments.