Graph-based collaborative filtering for recommendation has attracted great attention recently, due to its effectiveness of capturing high-order proximity among users and items. To further improve its model robustness and alleviate label-sparsity issue, contrastive learning has been introduced to polish user and item representation by contrasting different views of user/item nodes, learning necessary and robust representation for recommendation. However, we argue that prior contrastive learning approaches only explore its unsupervised intrinsic nature as a plug-in without leveraging available user-item interactions, failing to exploit the huge potential of contrastive learning. In this paper, to alleviate the above issues, we propose Hybrid Contrastive Learning for graph-based recommendation that integrates unsupervised and supervised contrastive learning. Specifically, to improve model robustness, we first present bipartite graph augmentation operations from the perspectives of node attributes and topology to generate incomplete and noisy graph views. Then, we propose a hybrid contrastive learning module that conducts unsupervised and supervised contrastive learning together. Last, we present an approach to perform hybrid contrastive learning permutationally among multiple views. Extensive experiments show that our proposed model not only outperforms state-of-the-art baselines significantly on two public datasets and one internal dataset, but also demonstrates superiority regarding to model robustness over other strong baselines.