Semi-supervised learning uses labeled and unlabeled data from known classes for training, assuming the test data contains only those classes. However, in real-world scenarios, new classes can appear. Generalized Category Discovery (GCD) extends SSL to handle unlabeled samples that may belong to both known and unknown categories. The challenge arises from the lack of prior information about the unknown categories. We propose to generate unknown samples to address the GCD problem, called Generalized Category Discovery with Unknown Sample Generation (GCDUSG). Since the number of unknown categories is uncertain, we propose a prototype alignment method to estimate both the class numbers and pseudo-labels for unlabeled samples, thereby enabling us to learn the unknown prototypes. We have developed a process for generating realistic and discriminative unknown samples based on the known-unknown relationships between known and unknown prototypes. We generate realistic and discriminative unknown samples leveraging the known-unknown relationships. We achieve this by minimizing the class-wise Maximum Mean Discrepancy distance between the generated samples and the selected unknown samples. To account for the pseudo-labels assigned to unlabeled samples, we train a classifier using all samples, incorporating a pseudo-label supervision loss to mitigate the impact of potentially erroneous labels. This comprehensive training equips the classifier to effectively handle both known and unknown classes during testing. Extensive experiments conducted on benchmark datasets demonstrate the effectiveness of our approach.