Unsupervised visible-infrared person re-identification is a challenging task due to the large modality gap and the unavailability of cross-modality correspondences. Cross-modality correspondences are very crucial to bridge the modality gap. Some existing works try to mine cross-modality correspondences, but they focus only on local information. They do not fully exploit the global relationship across identities, thus limiting the quality of the mined correspondences. Worse still, the number of clusters of the two modalities is often inconsistent, exacerbating the unreliability of the generated correspondences. In response, we devise a Progressive Graph Matching method to globally mine cross-modality correspondences under cluster imbalance scenarios. PGM formulates correspondences mining as a graph matching process and considers the global information by minimizing the global matching cost, where the matching cost measures the dissimilarity of clusters. Besides, PGM adopts a progressive strategy to address the imbalance issue with multiple dynamic matching processes. Based on PGM, we design an Alternate Cross Contrastive Learning (ACCL) module to reduce the modality gap with the mined cross-modality correspondences, while mitigating the effect of noise in correspondences through an alternate scheme. Extensive experiments demonstrate the reliability of the generated correspondences and the effectiveness of our method.