Abstract Hashing approach becomes popular for fast similarity search in many large scale applications. Real world data are usually with multiple modalities or having different representations from multiple sources. Various hashing methods have been proposed to generate compact binary codes from multi-modal data. However, most existing multimodal hashing techniques assume that each data example appears in all modalities, or at least there is one modality containing all data examples. But in real applications, it is often the case that every modality suffers from the missing of some data and therefore results in many partial examples, i.e., examples with some modalities missing. In this paper, we present a novel hashing approach to deal with Partial Multi-Modal data. In particular, the hashing codes are learned by simultaneously ensuring the data consistency among different modalities via latent subspace learning, and preserving data similarity within the same modality through graph Laplacian. We then further improve the codes via orthogonal rotation based on the orthogonal invariant property of our formulation. Experiments on two multi-modal datasets demonstrate the superior performance of the proposed approach over several state-of-the-art multi-modal hashing methods.