Continual Learning is considered a key step toward next-generation Artificial Intelligence. Among various methods, replay-based approaches that maintain and replay a small episodic memory of previous samples are one of the most successful strategies against catastrophic forgetting. However, since forgetting is inevitable given bounded memory and unbounded tasks, how to forget is a problem continual learning must address. Therefore, beyond simply avoiding catastrophic forgetting, an under-explored issue is how to reasonably forget while ensuring the merits of human memory, including 1. storage efficiency, 2. generalizability, and 3. some interpretability. To achieve these simultaneously, our paper proposes a new saliency-augmented memory completion framework for continual learning, inspired by recent discoveries in memory completion separation in cognitive neuroscience. Specifically, we innovatively propose to store the part of the image most important to the tasks in episodic memory by saliency map extraction and memory encoding. When learning new tasks, previous data from memory are inpainted by an adaptive data generation module, which is inspired by how humans complete episodic memory. The module's parameters are shared across all tasks and it can be jointly trained with a continual learning classifier as bilevel optimization. Extensive experiments on several continual learning and image classification benchmarks demonstrate the proposed method's effectiveness and efficiency.