This paper introduces the Definite Finite Automaton augmented large language model (DFA-LLM), a novel framework designed to enhance the capabilities of conversational agents using large language models (LLMs). Traditional LLMs face challenges in generating regulated and compliant responses in special scenarios with predetermined response guidelines, like the emotional support and customer service. Our framework addresses these challenges by embedding a Definite Finite Automaton (DFA), learned from training dialogues, within the LLM. This structured approach enables the LLM to adhere to a deterministic response pathway, guided by the DFA. The advantages of DFA-LLM include an interpretable structure through human-readable DFA, context-aware retrieval for responses in conversations, plug-and-play compatibility with existing LLMs. Extensive benchmarks validate DFA-LLM's effectiveness, indicating its potential as a valuable contribution to the conversational agent.