The inconsistent distribution and representation of image and text make it quite challenging to measure their similarity, and construct correlation between them. Inspired by neural machine translation to establish a corresponding relationship between two entirely different languages, we attempt to treat images as a special kind of language to provide visual descriptions, so that translation can be conduct between bilingual pair of image and text to effectively explore cross-modal correlation. Thus, we propose Cross-modal Bidirectional Translation (CBT) approach, and further explore the utilization of reinforcement learning to improve the translation process. First, a cross-modal translation mechanism is proposed, where image and text are treated as bilingual pairs, and cross-modal correlation can be effectively captured in both feature spaces of image and text by bidirectional translation training. Second, cross-modal reinforcement learning is proposed to perform a bidirectional game between image and text, which is played as a round to promote the bidirectional translation process. Besides, both inter-modality and intra-modality reward signals can be extracted to provide complementary clues for boosting cross-modal correlation learning. Experiments are conducted to verify the performance of our proposed approach on cross-modal retrieval, compared with 11 state-of-the-art methods on 3 datasets.