Text-image cross-modal retrieval is a challenging task in the field of language and vision. Most previous approaches independently embed images and sentences into a joint embedding space and compare their similarities. However, previous approaches rarely explore the interactions between images and sentences before calculating similarities in the joint space. Intuitively, when matching between images and sentences, human beings would alternatively attend to regions in images and words in sentences, and select the most salient information considering the interaction between both modalities. In this paper, we propose Cross-modal Adaptive Message Passing (CAMP), which adaptively controls the information flow for message passing across modalities. Our approach not only takes comprehensive and fine-grained cross-modal interactions into account, but also properly handles negative pairs and irrelevant information with an adaptive gating scheme. Moreover, instead of conventional joint embedding approaches for text-image matching, we infer the matching score based on the fused features, and propose a hardest negative binary cross-entropy loss for training. Results on COCO and Flickr30k significantly surpass state-of-the-art methods, demonstrating the effectiveness of our approach.