This paper introduces a novel approach using Large Language Models (LLMs) integrated into an agent framework for flexible and effective personal mobility generation. LLMs overcome the limitations of previous models by effectively processing semantic data and offering versatility in modeling various tasks. Our approach addresses three research questions: aligning LLMs with real-world urban mobility data, developing reliable activity generation strategies, and exploring LLM applications in urban mobility. The key technical contribution is a novel LLM agent framework that accounts for individual activity patterns and motivations, including a self-consistency approach to align LLMs with real-world activity data and a retrieval-augmented strategy for interpretable activity generation. We evaluate our LLM agent framework and compare it with state-of-the-art personal mobility generation approaches, demonstrating the effectiveness of our approach and its potential applications in urban mobility. Overall, this study marks the pioneering work of designing an LLM agent framework for activity generation based on real-world human activity data, offering a promising tool for urban mobility analysis.