Desires motivate humans to interact autonomously with the complex world. In contrast, current AI agents require explicit task specifications, such as instructions or reward functions, which constrain their autonomy and behavioral diversity. In this paper, we introduce a Desire-driven Autonomous Agent (D2A)that canenable a large language model (LLM) to autonomously propose and select tasks, motivated by satisfying its multi-dimensional desires. Specifically, the motivational framework of D2A is mainly constructed by a dynamic Value System, inspired by the Theory of Needs. It incorporates an understanding of human-like desires, such as the need for social interaction, personal fulfillment, and self-care. At each step, the agent evaluates the value of its current state, proposes a set of candidate activities, and selects the one that best aligns with its intrinsic motivations. We conduct experiments on Concordia, a text-based simulator, to demonstrate that our agent generates coherent, contextually relevant daily activities while exhibiting variability and adaptability similar to human behavior. A comparative analysis with other LLM-based agents demonstrates that our approach significantly enhances the rationality of the simulated activities.