Identifying cell types is one of the main goals of single-cell RNA sequencing (scRNA-seq) analysis, and clustering is a common method for this item. However, the massive amount of data and the excess noise level bring challenge for single cell clustering. To address this challenge, in this paper, we introduced a novel method named single-cell clustering based on denoising autoencoder and graph convolution network (scCDG), which consists of two core models. The first model is a denoising autoencoder (DAE) used to fit the data distribution for data denoising. The second model is a graph autoencoder using graph convolution network (GCN), which projects the data into a low-dimensional space (compressed) preserving topological structure information and feature information in scRNA-seq data simultaneously. Extensive analysis on seven real scRNA-seq datasets demonstrate that scCDG outperforms state-of-the-art methods in some research sub-fields, including single cell clustering, visualization of transcriptome landscape, and trajectory inference.