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Contrastive learning has been adopted as a core method for unsupervised visual representation learning. Without human annotation, the common practice is to perform an instance discrimination task: Given a query image crop, this task labels crops from the same image as positives, and crops from other randomly sampled images as negatives. An important limitation of this label assignment strategy is that it can not reflect the heterogeneous similarity between the query crop and each crop from other images, taking them as equally negative, while some of them may even belong to the same semantic class as the query. To address this issue, inspired by consistency regularization in semi-supervised learning on unlabeled data, we propose Consistent Contrast (CO2), which introduces a consistency regularization term into the current contrastive learning framework. Regarding the similarity of the query crop to each crop from other images as "unlabeled", the consistency term takes the corresponding similarity of a positive crop as a pseudo label, and encourages consistency between these two similarities. Empirically, CO2 improves Momentum Contrast (MoCo) by 2.9% top-1 accuracy on ImageNet linear protocol, 3.8% and 1.1% top-5 accuracy on 1% and 10% labeled semi-supervised settings. It also transfers to image classification, object detection, and semantic segmentation on PASCAL VOC. This shows that CO2 learns better visual representations for these downstream tasks.