The Structured Dialogue System, referred to as SuDoSys, is an innovative Large Language Model (LLM)-based chatbot designed to provide psychological counseling. SuDoSys leverages the World Health Organization (WHO)'s Problem Management Plus (PM+) guidelines to deliver stage-aware multi-turn dialogues. Existing methods for employing an LLM in multi-turn psychological counseling typically involve direct fine-tuning using generated dialogues, often neglecting the dynamic stage shifts of counseling sessions. Unlike previous approaches, SuDoSys considers the different stages of counseling and stores essential information throughout the counseling process, ensuring coherent and directed conversations. The system employs an LLM, a stage-aware instruction generator, a response unpacker, a topic database, and a stage controller to maintain dialogue flow. In addition, we propose a novel technique that simulates counseling clients to interact with the evaluated system and evaluate its performance automatically. When assessed using both objective and subjective evaluations, SuDoSys demonstrates its effectiveness in generating logically coherent responses. The system's code and program scripts for evaluation are open-sourced.