In recent years, Cross-Modal Hashing (CMH) has aroused much attention due to its fast query speed and efficient storage. Previous literatures have achieved promising results for Cross-Modal Retrieval (CMR) by discovering discriminative hash codes and modality-specific hash functions. Nonetheless, most existing CMR works are subjected to some restrictions: 1) It is assumed that data of different modalities are fully paired, which is impractical in real applications due to sample missing and false data alignment, and 2) binary regression targets including the label matrix and binary codes are too rigid to effectively learn semantic-preserving hash codes and hash functions. To address these problems, this paper proposes an Adaptive Marginalized Semantic Hashing (AMSH) method which not only enhances the discrimination of latent representations and hash codes by adaptive margins, but also can be used for both paired and unpaired CMR. As a two-step method, in the first step, AMSH generates semantic-aware modality-specific latent representations with adaptively marginalized labels, which enlarges the distances between different classes, and exploits the labels to preserve the inter-modal and intra-modal semantic similarities into latent representations and hash codes. In the second step, adaptive margin matrices are embedded into the hash codes, and enlarge the gaps between positive and negative bits, which improves the discrimination and robustness of hash functions. On this basis, AMSH generates similarity-preserving hash codes and robust hash functions without strict one-to-one data correspondence requirement. Experiments are conducted on several benchmark datasets to demonstrate the superiority and flexibility of AMSH over some state-of-the-art CMR methods.