In this article, we investigate a novel but insufficiently studied issue, unpaired multi-view clustering (UMC), where no paired observed samples exist in multi-view data, and the goal is to leverage the unpaired observed samples in all views for effective joint clustering. Existing methods in incomplete multi-view clustering usually utilize the sample pairing relationship between views to connect the views for joint clustering, but unfortunately, it is invalid for the UMC case. Therefore, we strive to mine a consistent cluster structure between views and propose an effective method, namely selective contrastive learning for UMC (scl-UMC), which needs to solve the following two challenging issues: 1) uncertain clustering structure under no supervision information and 2) uncertain pairing relationship between the clusters of views. Specifically, for the first one, we design an inner-view (IV) selective contrastive learning module to enhance the clustering structures and alleviate the uncertainty, which selects confident samples near the cluster centroids to perform contrastive learning in each view. For the second one, we design a cross-view (CV) selective contrastive learning module to first iteratively match the clusters between views and then tighten the matched clusters. Also, we utilize mutual information to further enhance the correlation of the matched clusters between views. Extensive experiments show the efficiency of our methods for UMC, compared with the state-of-the-art methods.