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Complementary-label learning (CLL) is widely used in weakly supervised classification, but it faces a significant challenge in real-world datasets when confronted with class-imbalanced training samples. In such scenarios, the number of samples in one class is considerably lower than in other classes, which consequently leads to a decline in the accuracy of predictions. Unfortunately, existing CLL approaches have not investigate this problem. To alleviate this challenge, we propose a novel problem setting that enables learning from class-imbalanced complementary labels for multi-class classification. To tackle this problem, we propose a novel CLL approach called Weighted Complementary-Label Learning (WCLL). The proposed method models a weighted empirical risk minimization loss by utilizing the class-imbalanced complementary labels, which is also applicable to multi-class imbalanced training samples. Furthermore, we derive an estimation error bound to provide theoretical assurance. To evaluate our approach, we conduct extensive experiments on several widely-used benchmark datasets and a real-world dataset, and compare our method with existing state-of-the-art methods. The proposed approach shows significant improvement in these datasets, even in the case of multiple class-imbalanced scenarios. Notably, the proposed method not only utilizes complementary labels to train a classifier but also solves the problem of class imbalance.