Deep clustering has made remarkable progress in recent years. However, most existing deep clustering methods assume that distributions of different clusters are balanced or roughly balanced, which are not consistent with the common long-tailed distributions in reality. In nature, the datasets often follow long-tailed distributions, leading to biased models being trained with significant performance drop. Despite the widespread proposal of many long-tailed learning approaches with supervision information, research on long-tailed deep clustering remains almost uncharted. Unaware of the data distribution and sample labels, long-tailed deep clustering is highly challenging. To tackle this problem, we propose a novel contrastive mixup method for long-tailed deep clustering, named ConMix. The proposed method makes innovations to mixup representations in contrastive learning to enhance deep clustering in long-tailed scenarios. Neural networks trained with ConMix can learn more discriminative representations, thus achieve better long-tailed deep clustering performance. We theoretically prove that ConMix works through re-balancing loss for classes with different long-tailed degree. We evaluate our method on widely used benchmark datasets with different imbalance ratios, suggesting it outperforms many state-of-the-art deep clustering approaches. The code is available at https://github.com/LZX-001/ConMix.