Recent research in biology has shifted the focus toward single-cell data analysis. The new single-cell technologies have allowed us to monitor and characterize cells in early embryonic stage and in heterogeneous tumor tissue. However, current single-cell RNA sequencing (scRNA-seq) technologies still need to overcome significant challenges to ensure accurate measurement of gene expression. One critical challenge is to address the dropout event. Due to the low amount of starting material, a large portion of expression values in scRNA-seq data is missing and reported as zeros. These missing values can greatly affect the accuracy of downstream analysis. Here we introduce scIRN, a neural network-based approach, that can reliably recover the missing values in single-cell data and thus can effectively improve the performance of downstream analyses. To impute the dropouts in single-cell data, we build a neural network that consists of two sub-networks: imputation sub-network and quality assessment sub-network. We compare scIRN with state-of-the-art imputation methods using 10 scRNA-seq datasets. In our extensive analysis, scIRN outperforms existing imputation methods in improving the identification of cell sub-populations and the quality of visualizing transcriptome landscape.