Large language models (LLMs) have been widely recognized as transformative technology due to their capabilities to understand and generate natural language text, including plans with some limited reasoning capabilities. LLM-based agents derive their autonomy from the capabilities of LLMs, which enable them to autonomously break down the given goal into a set of manageable tasks and orchestrate the task execution to fulfill the goal. Despite the huge efforts put into building LLM-based autonomous agents, the architecture design of the agents has not yet been systematically explored. Also, while there are significant benefits of using autonomous agents for planning and execution, there are serious considerations regarding responsible AI related software quality attributes, such as security and accountability. Therefore, this paper presents a pattern-oriented reference architecture that serves as architecture design guidelines and enables responsible-AI-by-design when designing LLM-based autonomous agents. We evaluate the completeness and utility of the proposed reference architecture by mapping it to the architecture of two real-world agents.