To achieve efficient cross-modal retrieval, cross-modal hashing have gained significant attention due to its advantages of low storage cost and high query efficiency. Existing hashing methods typically learn unified hash codes for different modalities in a common Hamming space, which often requires abstracting the raw data. This abstraction might disrupt the structural integrity of modality-specific features, leading to the loss of modality-specific information and consequently affecting retrieval performance. To better preserve and utilize modality-specific information, we propose a novel cross-modal hashing method called Modality-Specific Hashing (MSH), which aims to transform cross-modal retrieval into single-modal retrieval by learning the mapping relationships between different modal features. Specifically, in representation learning phase, we construct a cycle generative adversarial network (CycleGAN) that effectively establishes mapping relationships among different modality features through learning their bidirectional transformations. In hashing learning phase, we adopt a modality-specific weight-sharing strategy to learn unified hash codes for each specific modality. These generated hash codes not only encapsulate semantic information but also retain modality-specific information, enabling more comprehensive and precise retrieval. Extensive experiments conducted on two cross-modal benchmark datasets demonstrate that our model outperforms several state-of-the-art baselines.