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Existing research into online multi-label classification, such as online sequential multi-label extreme learning machine (OSML-ELM) and stochastic gradient descent (SGD), has achieved promising performance. However, these works do not take label dependencies into consideration and lack a theoretical analysis of loss functions. Accordingly, we propose a novel online metric learning paradigm for multi-label classification to fill the current research gap. Generally, we first propose a new metric for multi-label classification which is based on $k$-Nearest Neighbour ($k$NN) and combined with large margin principle. Then, we adapt it to the online settting to derive our model which deals with massive volume ofstreaming data at a higher speed online. Specifically, in order to learn the new $k$NN-based metric, we first project instances in the training dataset into the label space, which make it possible for the comparisons of instances and labels in the same dimension. After that, we project both of them into a new lower dimension space simultaneously, which enables us to extract the structure of dependencies between instances and labels. Finally, we leverage the large margin and $k$NN principle to learn the metric with an efficient optimization algorithm. Moreover, we provide theoretical analysis on the upper bound of the cumulative loss for our method. Comprehensive experiments on a number of benchmark multi-label datasets validate our theoretical approach and illustrate that our proposed online metric learning (OML) algorithm outperforms state-of-the-art methods.