Partial Multi-Label learning (PML) learns from the ambiguous data where each instance is associated with a candidate label set, where only a part is correct. The key to solve such problem is to disambiguate the candidate label sets and identify the correct assignments between instances and their ground-truth labels. In this paper, we interpret such assignments as instance-to-label matchings, and formulate the task of PML as a matching selection problem. To model such problem, we propose a novel grapH mAtching based partial muLti-label lEarning (HALE) framework, where Graph Matching scheme is incorporated owing to its good performance of exploiting the instance and label relationship. Meanwhile, since conventional one-to-one graph matching algorithm does not satisfy the constraint of PML problem that multiple instances may correspond to multiple labels, we extend the traditional probabilistic graph matching algorithm from one-to-one constraint to many-to-many constraint, and make the proposed framework to accommodate to the PML problem. Moreover, to improve the performance of predictive model, both the minimum error reconstruction and k-nearest-neighbor weight voting scheme are employed to assign more accurate labels for unseen instances. Extensive experiments on various data sets demonstrate the superiority of our proposed method.