Product review generation is an important task in recommender systems, which could provide explanation and persuasiveness for the recommendation. Recently, Large Language Models (LLMs, e.g., ChatGPT) have shown superior text modeling and generating ability, which could be applied in review generation. However, directly applying the LLMs for generating reviews might be troubled by the ``polite'' phenomenon of the LLMs and could not generate personalized reviews (e.g., negative reviews). In this paper, we propose Review-LLM that customizes LLMs for personalized review generation. Firstly, we construct the prompt input by aggregating user historical behaviors, which include corresponding item titles and reviews. This enables the LLMs to capture user interest features and review writing style. Secondly, we incorporate ratings as indicators of satisfaction into the prompt, which could further improve the model's understanding of user preferences and the sentiment tendency control of generated reviews. Finally, we feed the prompt text into LLMs, and use Supervised Fine-Tuning (SFT) to make the model generate personalized reviews for the given user and target item. Experimental results on the real-world dataset show that our fine-tuned model could achieve better review generation performance than existing close-source LLMs.