Large language models exhibit aspects of human-level intelligence that catalyze their application as human-like agents in domains such as social simulations, human-machine interactions, and collaborative multi-agent systems. However, the absence of distinct personalities, such as displaying ingratiating behaviors, inconsistent opinions, and uniform response patterns, diminish LLMs utility in practical applications. Addressing this, the development of personality traits in LLMs emerges as a crucial area of research to unlock their latent potential. Existing methods to personify LLMs generally involve strategies like employing stylized training data for instruction tuning or using prompt engineering to simulate different personalities. These methods only capture superficial linguistic styles instead of the core of personalities and are therefore not stable. In this study, we propose PersLLM, integrating psychology-grounded principles of personality: social practice, consistency, and dynamic development, into a comprehensive training methodology. We incorporate personality traits directly into the model parameters, enhancing the model's resistance to induction, promoting consistency, and supporting the dynamic evolution of personality. Single-agent evaluation validates our method's superiority, as it produces responses more aligned with reference personalities compared to other approaches. Case studies for multi-agent communication highlight its benefits in enhancing opinion consistency within individual agents and fostering collaborative creativity among multiple agents in dialogue contexts, potentially benefiting human simulation and multi-agent cooperation. Additionally, human-agent interaction evaluations indicate that our personified models significantly enhance interactive experiences, underscoring the practical implications of our research.