Recent years, graph contrastive learning (GCL), which aims to learn representations from unlabeled graphs, has made great progress. However, the existing GCL methods mostly adopt human-designed graph augmentations, which are sensitive to various graph datasets. In addition, the contrastive losses originally developed in computer vision have been directly applied to graph data, where the neighboring nodes are regarded as negatives and consequently pushed far apart from the anchor. However, this is contradictory with the homophily assumption of networks that connected nodes often belong to the same class and should be close to each other. In this work, we propose an end-to-end automatic GCL method, named NCLA to apply neighbor contrastive learning on learnable graph augmentation. Several graph augmented views with adaptive topology are automatically learned by the multi-head graph attention mechanism, which can be compatible with various graph datasets without prior domain knowledge. In addition, a neighbor contrastive loss is devised to allow multiple positives per anchor by taking network topology as the supervised signals. Both augmentations and embeddings are learned end-to-end in the proposed NCLA. Extensive experiments on the benchmark datasets demonstrate that NCLA yields the state-of-the-art node classification performance on self-supervised GCL and even exceeds the supervised ones, when the labels are extremely limited. Our code is released at https://github.com/shenxiaocam/NCLA.