We tackle the generalized category discovery (GCD) problem, which aims to discover novel classes in unlabeled datasets by leveraging the knowledge of known classes. Previous works utilize the known class knowledge through shared representation spaces. Despite their progress, our analysis experiments show that novel classes can achieve impressive clustering results on the feature space of a known class pre-trained model, suggesting that existing methods may not fully utilize known class knowledge. To address it, we introduce a novel concept learning framework for GCD, named ConceptGCD, that categorizes concepts into two types: derivable and underivable from known class concepts, and adopts a stage-wise learning strategy to learn them separately. Specifically, our framework first extracts known class concepts by a known class pre-trained model and then produces derivable concepts from them by a generator layer with a covariance-augmented loss. Subsequently, we expand the generator layer to learn underivable concepts in a balanced manner ensured by a concept score normalization strategy and integrate a contrastive loss to preserve previously learned concepts. Extensive experiments on various benchmark datasets demonstrate the superiority of our approach over the previous state-of-the-art methods. Code will be available soon.