Personalized large language models (LLMs) have attracted great attention in many applications, such as intelligent education and emotional support. Most work focuses on controlling the character settings based on the profile (e.g., age, skill, experience, and so on). Conversely, the psychological theory-based personality traits with implicit expression and behavior are not well modeled, limiting their potential application in more specialized fields such as the psychological counseling agents. In this paper, we propose a mixture of experts (MoE)-based personalized LLMs, named P-tailor, to model the Big Five Personality Traits. Particularly, we learn specialized LoRA experts to represent various traits, such as openness, conscientiousness, extraversion, agreeableness and neuroticism. Then, we integrate P-Tailor with a personality specialization loss, promoting experts to specialize in distinct personality traits, thereby enhancing the efficiency of model parameter utilization. Due to the lack of datasets, we also curate a high-quality personality crafting dataset (PCD) to learn and develop the ability to exhibit different personality traits across various topics. We conduct extensive experiments to verify the great performance and effectiveness of P-Tailor in manipulation of the fine-grained personality traits of LLMs.