This paper proposes a novel Large Language Model Agent-Guided (LLM-AG) multi-agent framework for adaptive traffic signal control, aiming to alleviate urban traffic congestion effectively. Unlike existing multi-agent reinforcement learning (MARL) methods such as MA2C and LRUA, which suffer from high communication overhead and limited global coordination, our approach integrates a centralized LLM agent that provides comprehensive predictive traffic inflow information directly to local intersection agents. By enriching local state representations, LLM-AG significantly enhances global coordination and scalability. Extensive simulation experiments demonstrate substantial performance improvements over state-of-the-art methods in queue length, vehicle speed, and intersection delay, confirming the effectiveness of our proposed framework.