In this article, a new unsupervised contrastive clustering (CC) model is introduced, namely, image CC with self-learning pairwise constraints (ICC-SPC). This model is designed to integrate pairwise constraints into the CC process, enhancing the latent representation learning and improving clustering results for image data. The incorporation of pairwise constraints helps reduce the impact of false negatives and false positives in contrastive learning, while maintaining robust cluster discrimination. However, obtaining prior pairwise constraints from unlabeled data directly is quite challenging in unsupervised scenarios. To address this issue, ICC-SPC designs a pairwise constraints learning module. This module autonomously learns pairwise constraints among data samples by leveraging consensus information between latent representation and pseudo-labels, which are generated by the clustering algorithm. Consequently, there is no requirement for labeled images, offering a practical resolution to the challenge posed by the lack of sufficient supervised information in unsupervised clustering tasks. ICC-SPC's effectiveness is validated through evaluations on multiple benchmark datasets. This contribution is significant, as we present a novel framework for unsupervised clustering by integrating contrastive learning with self-learning pairwise constraints.