Recent advancements in Large Language Models (LLMs) have shown remarkable capabilities in reasoning, prompting a surge in research aimed at developing trustworthy LLMs. The emergence of LLM-based agents has garnered considerable attention, yet their trustworthiness remains an under-explored area. As agents can directly interact with the physical environment in everyday human activities, their reliability and safety is critical. This paper presents an Agent-Constitution-based agent framework, TrustAgent, an initial investigation into improving the safety dimension of trustworthiness in LLM-based agents. This framework consists of threefold strategies – pre-planning strategy which injects safety knowledge to the model prior to plan generation, in-planning strategy which bolsters safety during plan generation, and post-planning strategy which ensures safety by post-planning inspection. Through experimental analysis, we demonstrate how these approaches can effectively elevate an LLM agent’s safety by identifying and preventing potential challenges. Furthermore, we explore the intricate relationships between safety and helpfulness, and model’s reasoning ability and its efficacy as a safe agent. We argue that a robust reasoning ability is a fundamental prerequisite for an LLM to function safely as an agent. This paper underscores the imperative of integrating safety awareness and trustworthiness into the design and deployment of LLM-based agents, not only to enhance their performance but also to ensure their responsible integration into human-centric environments.