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Recently, domain-specific PLMs have been proposed to boost the task performance of specific domains (e.g., biomedical and computer science) by continuing to pre-train general PLMs with domain-specific corpora. However, this Domain-Adaptive Pre-Training (DAPT; Gururangan et al. (2020)) tends to forget the previous general knowledge acquired by general PLMs, which leads to a catastrophic forgetting phenomenon and sub-optimal performance. To alleviate this problem, we propose a new framework of General Memory Augmented Pre-trained Language Model (G-MAP), which augments the domain-specific PLM by a memory representation built from the frozen general PLM without losing any general knowledge. Specifically, we propose a new memory-augmented layer, and based on it, different augmented strategies are explored to build the memory representation and then adaptively fuse it into the domain-specific PLM. We demonstrate the effectiveness of G-MAP on various domains (biomedical and computer science publications, news, and reviews) and different kinds (text classification, QA, NER) of tasks, and the extensive results show that the proposed G-MAP can achieve SOTA results on all tasks.