Class incremental learning (CIL) is a specific scenario in incremental learning. It aims to continuously learn new classes from the data stream, which suffers from the challenge of catastrophic forgetting. Inspired by the human hippocampus, the CIL method for replaying episodic memory offers a promising solution. However, the limited buffer budget restricts the number of old class samples that can be stored, resulting in an imbalance between new and old class samples during each incremental learning stage. This imbalance adversely affects the mitigation of catastrophic forgetting. Therefore, we propose a novel CIL method based on multi-granularity balance strategy (MGBCIL), which is inspired by the three-way granular computing in human problem-solving. In order to mitigate the adverse effects of imbalances on catastrophic forgetting at fine-, medium-, and coarse-grained levels during training, MGBCIL introduces specific strategies across the batch, task, and decision stages. Specifically, a weighted cross-entropy loss function with a smoothing factor is proposed for batch processing. In the process of task updating and classification decision, contrastive learning with different anchor point settings is employed to promote local and global separation between new and old classes. Additionally, the knowledge distillation technology is used to preserve knowledge of the old classes. Experimental evaluations on CIFAR-10 and CIFAR-100 datasets show that MGBCIL outperforms other methods in most incremental settings. Specifically, when storing 3 exemplars on CIFAR-10 with Base2 Inc2 setting, the average accuracy is improved by up to 9.59% and the forgetting rate is reduced by up to 25.45%.