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Single-cell RNA sequencing technology provides an opportunity to study gene expression at single-cell resolution. However, prevalent dropout events result in high data sparsity and noise that may obscure downstream analyses in single-cell transcriptomic studies. We propose a new method, G2S3, that imputes dropouts by borrowing information from adjacent genes in a sparse gene graph learned from gene expression profiles across cells. We applied G2S3 and ten existing imputation methods to eight single-cell transcriptomic datasets and compared their performance. Our results demonstrated that G2S3 has superior overall performance in recovering gene expression, identifying cell subtypes, reconstructing cell trajectories, identifying differentially expressed genes, and recovering gene regulatory and correlation relationships. Moreover, G2S3 is computationally efficient for imputation in large-scale single-cell transcriptomic datasets.