Reconstruction of gene regulatory networks from gene expression profile have been an important challenge task in system biology for decades. Recently, with the advancement of single cell RNA-seq technology, the studies in this field turn from bulk gene expression data to scRNA-seq data. However, the complexity of regulatory relationships and high noise in scRNA-seq introduce further challenges in addressing this issue. In this study, we proposed a flexible gene regulatory network reconstruction method based on autoencoder and graph attention network, called scGiant. scGiant incorporates autoencoder to capture the non-linear representation of genes with graph attention network to learn regulatory relationships among genes. To evaluate the performance of scGiant, we compared it with seven state-of-the-art GRN inference algorithms on four real single-cell RNA sequencing datasets, and the results demonstrate that scGiant is superior in accuracy and scalability. The inferred core GRN of CD8+ naïve T cells also demonstrates its potential in practical biological applications.