Recently, some contrastive learning methods have been proposed to simultaneously learn representations and clustering assignments, achieving significant improvements. However, these methods do not take the category information and clustering objective into consideration, thus the learned representations are not optimal for clustering and the performance might be limited. Towards this issue, we first propose a novel graph contrastive learning framework, and then apply it to the clustering task, resulting in the Graph Constrastive Clustering (GCC) method. Different from basic contrastive clustering that only assumes an image and its augmentation should share similar representation and clustering assignments, we lift the instancelevel consistency to the cluster-level consistency with the assumption that samples in one cluster and their augmentations should all be similar. Specifically, on the one hand, we propose the graph Laplacian based contrastive loss to learn more discriminative and clustering-friendly features. On the other hand, we propose a novel graph-based contrastive learning strategy to learn more compact clustering assignments. Both of them incorporate the latent category information to reduce the intra-cluster variance as well as increase the inter-cluster variance. Experiments on six commonly used datasets demonstrate the superiority of our proposed approach over the state-of-the-art methods.