Forgetting is the biggest problem of artificial neural networks in incremental learning and is thus called “catastrophic forgetting”. In contrast, humans can continuously acquire new knowledge and retain most of the frequently used old knowledge. This continuous “incremental learning” ability of human without extensive forgetting is related to the partitioned learning structure and memory replay ability of the human brain. To simulate this structure and ability, the study proposes an incremental learning approach of “recency-bias-avoiding partitioned incremental learning based on self-learning mask (SLM)”, or ASPIL for short. ASPIL involves the two stages of regional isolation and regional integration, which are alternately iterated to accomplish continuous incremental learning. Specifically, this study proposes the “Bayesian network (BN)-based sparse regional isolation” method to isolate the new learning process from the existing knowledge and thereby avoid the interference with the existing knowledge. For regional integration, SLM and dual-branch fusion (GBF) methods are proposed. The SLM method can accurately extracts new knowledge and improves the adaptability of the network to new knowledge, while the GBF method integrates the old and new knowledge to achieve the goal of fostering unified and high-precision cognition. During training, a regularization term for Margin Loss is proposed to avoid the “recency bias”, thereby ensuring the further balance of the old knowledge and the avoidance of the bias towards the new knowledge. To evaluate the effectiveness of the proposed method, this study also presents systematic ablation experiments performed on the standard incremental learning datasets CIFAR-100 and miniImageNet and compares the proposed method with a series of well-known state-of-the-art methods. The experimental results show that the method proposed in this study improves the memory ability of the artificial neural network and outperforms the latest well-known methods by more than 5.27% in average identification rate.