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Multi-modal reasoning in visual question answering (VQA) has witnessed rapid progress recently. However, most reasoning models heavily rely on shortcuts learned from training data, which prevents their usage in challenging real-world scenarios. In this paper, we propose a simple but effective cross-modal contrastive learning strategy to get rid of the shortcut reasoning caused by imbalanced annotations and improve the overall performance. Different from existing contrastive learning with complex negative categories on coarse (Image, Question, Answer) triplet level, we leverage the correspondences between the language and image modalities to perform finer-grained cross-modal contrastive learning. We treat each Question-Answer (QA) pair as a whole, and differentiate between images that conform with it and those against it. To alleviate the issue of sampling bias, we further build connected graphs among images. For each positive pair, we regard the images from different graphs as negative samples and deduct the version of multi-positive contrastive learning. To our best knowledge, it is the first paper that reveals a general contrastive learning strategy without delicate hand-craft rules can contribute to robust VQA reasoning. Experiments on several mainstream VQA datasets demonstrate our superiority compared to the state of the arts. Code is available at \url{https://github.com/qizhust/cmcl_vqa_pl}.