Code refactoring is a critical task for improving software quality, but it is traditionally a manual, time-consuming process. This paper demonstrates an approach to automate project-level code refactoring using Large Language Models (LLMs). The key idea is to iteratively identify methods with high cyclomatic complexity, and then use LLMs to generate refactored implementations that reduce complexity. Our evaluation using 17 open-source projects shows that the proposed automated refactoring can reduce average cyclomatic complexity by up to 10.4% within 20 iterations. These results suggest that automated project-level code refactoring is feasible using LLMs with tailored prompts.