The advent of the Web has brought about a paradigm shift in traditional economics, particularly in the digital economy era, enabling the precise recording and analysis of individual economic behavior. This has led to a growing emphasis on data-driven modeling in macroeconomics. In macroeconomic research, Agent-based modeling (ABM) emerged as an alternative, evolving through rule-based agents, machine learning-enhanced decision-making, and, more recently, advanced AI agents. However, the existing works are suffering from three main challenges when endowing agents with human-like decision-making, including agent heterogeneity, the influence of macroeconomic trends, and multifaceted economic factors. Large language models (LLMs) have recently gained prominence in offering autonomous human-like characteristics. Therefore, leveraging LLMs in macroeconomic simulation presents an opportunity to overcome traditional limitations. In this work, we take an early step in introducing a novel approach that leverages LLMs in macroeconomic simulation. We design prompt-engineering-driven LLM agents to exhibit human-like decision-making and adaptability in the economic environment, with the abilities of perception, reflection, and decision-making to address the abovementioned challenges. Simulation experiments on macroeconomic activities show that LLM-empowered agents can make realistic work and consumption decisions and emerge more reasonable macroeconomic phenomena than existing rule-based or AI agents. Our work demonstrates the promising potential to simulate macroeconomics based on LLM and its human-like characteristics.