This study presents a novel approach to Generative Class Incremental Learning (GCIL) by introducing the forgetting mechanism, aimed at dynamically managing class information for better adaptation to streaming data. GCIL is one of the hot topics in the field of computer vision, and this is considered one of the crucial tasks in society, specifically the continual learning of generative models. The ability to forget is a crucial brain function that facilitates continual learning by selectively discarding less relevant information for humans. However, in the field of machine learning models, the concept of intentionally forgetting has not been extensively investigated. In this study we aim to bridge this gap by incorporating the forgetting mechanisms into GCIL, thereby examining their impact on the models' ability to learn in continual learning. Through our experiments, we have found that integrating the forgetting mechanisms significantly enhances the models' performance in acquiring new knowledge, underscoring the positive role that strategic forgetting plays in the process of continual learning.