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Accurate assessment of personality traits is crucial for effective psycho-counseling, yet traditional methods like self-report questionnaires are time-consuming and biased. This study exams whether Large Language Models (LLMs) can predict the Big Five personality traits directly from counseling dialogues and introduces an innovative framework to perform the task. Our framework applies role-play and questionnaire-based prompting to condition LLMs on counseling sessions, simulating client responses to the Big Five Inventory. We evaluated our framework on 853 real-world counseling sessions, finding a significant correlation between LLM-predicted and actual Big Five traits, proving the validity of framework. Moreover, ablation studies highlight the importance of role-play simulations and task simplification via questionnaires in enhancing prediction accuracy. Meanwhile, our fine-tuned Llama3-8B model, utilizing Direct Preference Optimization with Supervised Fine-Tuning, achieves a 130.95% improvement, surpassing the state-of-the-art Qwen1.5-110B by 36.94% in personality prediction validity. In conclusion, LLMs can predict personality based on counseling dialogues. Our code and model are publicly available at \url{https://github.com/kuri-leo/BigFive-LLM-Predictor}, providing a valuable tool for future research in computational psychometrics.