We address the problem of generalized category discovery (GCD) that aims to partition a partially labeled collection of images; only a small part of the collection is labeled and the total number of target classes is unknown. To address this generalized image clustering problem, we revisit the mean-shift algorithm, i.e., a classic, powerful technique for mode seeking, and incorporate it into a contrastive learning framework. The proposed method, dubbed Contrastive Mean-Shift (CMS) learning, trains an embedding network to produce representations with better clustering properties by an iterative process of mean shift and contrastive update. Experiments demonstrate that our method, both in settings with and without the total number of clusters being known, achieves state-of-the-art performance on six public GCD benchmarks without bells and whistles.