Simulation plays a crucial role in addressing various challenges within social science. It offers extensive applications such as state prediction, phenomena explanation, and policy-making support, among others. In this work, we harness the human-like capabilities of large language models (LLMs) in sensing, reasoning, and behaving, and utilize these qualities to construct the S3 system (short for Social network Simulation System). Adhering to the widely employed agent-based simulation paradigm, we employ fine-tuning and prompt engineering techniques to ensure that the agent's behavior closely emulates that of a genuine human within the social network. Specifically, we simulate three pivotal aspects: emotion, attitude, and interaction behaviors. By endowing the agent in the system with the ability to perceive the informational environment and emulate human actions, we observe the emergence of population-level phenomena, including the propagation of information, attitudes, and emotions. We conduct an evaluation encompassing two levels of simulation, employing real-world social network data. Encouragingly, the results demonstrate promising accuracy. This work represents an initial step in the realm of social network simulation empowered by LLM-based agents. We anticipate that our endeavors will serve as a source of inspiration for the development of simulation systems within, but not limited to, social science.