The emergence of single-cell RNA sequencing (scRNA-seq) technologies has enabled us to measure the expression levels of thousands of genes at single-cell resolution. However, insufficient quantities of starting RNA in the individual cells cause significant dropout events, introducing a large number of zero counts in the expression matrix. To circumvent this, we developed an autoencoder-based sparse gene expression matrix imputation method. AutoImpute, which learns the inherent distribution of the input scRNA-seq data and imputes the missing values accordingly with minimal modification to the biologically silent genes. When tested on real scRNA-seq datasets, AutoImpute performed competitively wrt., the existing single-cell imputation methods, on the grounds of expression recovery from subsampled data, cell-clustering accuracy, variance stabilization and cell-type separability.