Generalized Category Discovery (GCD) focuses on classifying known categories while simultaneously discovering novel categories from unlabeled data. However, previous GCD methods face challenges due to inconsistent optimization objectives and category confusion. This leads to feature overlap and ultimately hinders performance on novel categories. To address these issues, we propose the Neural Collapse-inspired Generalized Category Discovery (NC-GCD) framework. By pre-assigning and fixing Equiangular Tight Frame (ETF) prototypes, our method ensures an optimal geometric structure and a consistent optimization objective for both known and novel categories. We introduce a Consistent ETF Alignment Loss that unifies supervised and unsupervised ETF alignment and enhances category separability. Additionally, a Semantic Consistency Matcher (SCM) is designed to maintain stable and consistent label assignments across clustering iterations. Our method achieves strong performance on multiple GCD benchmarks, significantly enhancing novel category accuracy and demonstrating its effectiveness.