Generalized category discovery (GCD) is a recently proposed open-world problem, which aims to automatically cluster partially labeled data. The main challenge is that the unlabeled data contain instances that are not only from known categories of the labeled data but also from novel categories. This leads traditional novel category discovery (NCD) methods to be incapacitated for GCD, due to their assumption of unlabeled data are only from novel categories. One effective way for GCD is applying self-supervised learning to learn discriminate representation for unlabeled data. However, this manner largely ignores underlying relationships between instances of the same concepts (e.g., class, super-class, and sub-class), which results in inferior representation learning. In this paper, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework, which can effectively improve clustering accuracy by alternately estimating underlying visual conceptions and learning conceptional representation. In addition, we design a dynamic conception generation and update mechanism, which is able to ensure consistent conception learning and thus further facilitate the optimization of DCCL. Extensive experiments show that DCCL achieves new state-of-the-art performances on six generic and fine-grained visual recognition datasets, especially on fine-grained ones. For example, our method significantly surpasses the best competitor by 16.2% on the new classes for the CUB-200 dataset. Code is available at https://github.com/TPCD/DCCL