Class incremental learning (CIL) is a crucial approach for AI models, yet it faces the challenge of catastrophic forgetting. The CIL method that replays episodic memory is a promising solution inspired by the hippocampus in humans. However, the limited buffer budget in CIL method constrains the number of stored exemplars from old classes, resulting in an imbalance between new and old samples in each incremental learning stage, thus it affects the resolution of catastrophic forgetting. Therefore, a novel CIL method based on the multi-granularity balance (MGBCIL) is proposed, which is inspired by the granular cognition mechanisms for human problem-solving. In order to mitigates the adverse impact of sample imbalance between new and old classes at fine-, medium-, and coarse-grained levels on addressing catastrophic forgetting, MGBCIL implements specific strategies during the batch, task, and decision stages. Specifically, a weighted cross-entropy loss with a smoothing factor is proposed for batch processing. During task updating and classification decision, contrastive learning with different anchor settings is introduced to promote both local and global separation between new and old classes. Meanwhile, knowledge distillation is used to retain the knowledge of old classes. Experimental results on CIFAR-10 and CIFAR-100 datasets demonstrate the superior performance of MGBCIL compared to other methods. The average accuracy is improved by up to 2.09%, while the forgetting rate is reduced by up to 4.41%.