Unsupervised domain adaptive (UDA) person reidentification (re-ID) is a challenging task due to the missing of labels for the target domain data. To handle this problem, some recent works adopt clustering algorithms to off-line generate pseudo labels, which can then be used as the supervision signal for on-line feature learning in the target domain. However, the offline generated labels often contain lots of noise that significantly hinders the discriminability of the on-line learned features, and thus limits the final UDA re-ID performance. To this end, we propose a novel approach, called Dual-Refinement, that jointly refines pseudo labels at the off-line clustering phase and features at the on-line training phase, to alternatively boost the label purity and feature discriminability in the target domain for more reliable re-ID. Specifically, at the off-line phase, a new hierarchical clustering scheme is proposed, which selects representative prototypes for every coarse cluster. Thus, labels can be effectively refined by using the inherent hierarchical information of person images. Besides, at the on-line phase, we propose an instant memory spread-out (IM-spread-out) regularization, that takes advantage of the proposed instant memory bank to store sample features of the entire dataset and enable spreadout feature learning over the entire training data instantly. Our Dual-Refinement method reduces the influence of noisy labels and refines the learned features within the alternative training process. Experiments demonstrate that our method outperforms the state-of-the-art methods by a large margin.