Most existing person re-identification (re-id) methods are designed based on the artificial closed-set assumption that the probe and gallery identities are exactly overlapped with a small search pool. This leads to poor scalability in real-world applications where the task is often to re-id a small set of target people (i.e., watch-list) among a large search pool with unknown ID overlap, namely, an open-set deployment setting. In this paper, we firstly propose a new person re-id setting called Watch-List based Open-Set (WLOS) person re-id, which is characterised by the above open-set deployment and a watch-list available at the training stage. Then, we address such a under-studied WLOS problem by formulating a novel Task Dedicated Deep Hashing (TDDH) approach which learning a purpose-specific deep hash model particularly for the given target people in an efficient end-to-end manner. Extensive experiments on three large-scale re-id benchmarks are conducted to demonstrate the advantages and superiority of the TDDH over a wide range of the state-of-the-art hashing and re-id methods under the more realistic open-set setting.