Large Language Models (LLMs), such as GPT3.5, have exhibited remarkable proficiency in comprehending and generating natural language. However, their unpersonalized generation paradigm may result in suboptimal user-specific outcomes. Typically, users converse differently based on their knowledge and preferences. This necessitates the task of enhancing user-oriented LLM which remains unexplored. While one can fully train an LLM for this objective, the resource consumption is unaffordable. Prior research has explored memory-based methods to store and retrieve knowledge to enhance generation without retraining for new queries. However, we contend that a mere memory module is inadequate to comprehend a user's preference, and fully training an LLM can be excessively costly. In this study, we propose a novel computational bionic memory mechanism, equipped with a parameter-efficient fine-tuning schema, to personalize LLMs. Our extensive experimental results demonstrate the effectiveness and superiority of the proposed approach. To encourage further research into this area, we are releasing a new conversation dataset generated entirely by LLM based on an open-source medical corpus, as well as our implementation code.