Single-cell RNA sequencing technology promotes the profiling of single-cell transcriptomes at an unprecedented throughput and resolution. However, in scRNA-seq studies, only a low amount of sequenced mRNA in each cell leads to missing detection for a portion of mRNA molecules, i.e. the dropout problem which hinders various downstream analyses. Therefore, it is necessary to develop robust and effective imputation methods for the increasing scRNA-seq data. In this study, we have developed an imputation method (GraphSCI) to impute the dropout events in scRNA-seq data based on the graph convolution networks. Extensive experiments demonstrated that GraphSCI outperforms other state-of-the-art methods for imputation on both simulated and real scRNA-seq data. Meanwhile, GraphSCI is able to accurately infer gene-to-gene relationships and the inferred gene-to-gene relationships could also provide powerful assistance for imputation dynamically during the training process, which is a key promotion of GraphSCI compared with other imputation algorithms.