Cross-view hashing has shown great potential for large-scale retrieval due to its superiority in terms of computation and storage. In real-world applications, data emerges in a streaming manner, e.g., new images and tags are uploaded to social media by users every day. Existing cross-view hashing methods have to retrain model on new multi-view data, which is time-consuming and not applicable in the real-world applications. To fill this gap, this paper proposes a new online cross-view hashing method, dubbed online unsupervised cross-view discrete hashing (OUCDH) that considers similarity preservation and quantization loss. OUCDH generates hash code as latent embedding shared by multiple views via matrix factorization. OUCDH can well preserve similarity among newly arriving data and old data with the help of anchor graph. An iterative efficient algorithm is developed for online optimization. OUCDH further updates hash code of old data to match that of newly arriving data in each iteration. Extensive experiments on three benchmarks demonstrate that the proposed OUCDH yields superior performance than existing state-of-the-art online cross-view hashing methods.