Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disease. Early and precise diagnosis of AD is crucial for timely intervention and treatment planning to alleviate the progressive neurodegeneration. However, most existing methods rely on single-modality data, which contrasts with the multifaceted approach used by medical experts. While some deep learning approaches process multi-modal data, they are limited to specific tasks with a small set of input modalities and cannot handle arbitrary combinations. This highlights the need for a system that can address diverse AD-related tasks, process multi-modal or missing input, and integrate multiple advanced methods for improved performance. In this paper, we propose ADAgent, the first specialized AI agent for AD analysis, built on a large language model (LLM) to address user queries and support decision-making. ADAgent integrates a reasoning engine, specialized medical tools, and a collaborative outcome coordinator to facilitate multi-modal diagnosis and prognosis tasks in AD. Extensive experiments demonstrate that ADAgent outperforms SOTA methods, achieving significant improvements in accuracy, including a 2.7% increase in multi-modal diagnosis, a 0.7% improvement in multi-modal prognosis, and enhancements in MRI and PET diagnosis tasks.