Refactoring is an important part of software development and maintenance. The scalability and maintainability of software systems are based on effective code refactoring. However, this process is still labor intensive, as it requires programmers to analyze the codebases in detail to avoid introducing new defects. In this paper, we take a step forward in automating the refactoring process of Haskell code by utilizing a large language model (LLM)-based multi-agent system. The objective of this research is to evaluate the effectiveness of LLM-based agents in performing structured and semantically accurate refactoring of Haskell code. Our proposed multi-agent system is based on specialized agents with distinct roles, including code analysis, refactoring execution, verification, and debugging. To test the effectiveness of the multi-agent system, we conducted evaluations using different open-source Haskell codebases. The results of the experiments show that the proposed LLM-based multi-agent system achieved an average reduction of 11.03% in code complexity, a 22.46% improvement in overall code quality, and a 13.27% increase in performance efficiency. Furthermore, memory allocation was optimized by up to 14.57%. These results highlight the capability of the LLM-based multi-agent system to manage refactoring tasks targeted toward functional programming paradigms. Our findings suggest that integrating LLM-based multi-agent systems into the refactoring of functional programming languages can enhance maintainability and support automated development workflows. The source code of our proposed system and the metrics results are publicly available on GitHub (https://github.com/GPT-Laboratory/Intelligent-Haskell-Code-Refactoring)