Vocal health plays a crucial role in peoples' lives, significantly impacting their communicative abilities and interactions. However, despite the global prevalence of voice disorders, many lack access to convenient diagnosis and treatment. This paper introduces VocalAgent, an audio large language model (LLM) to address these challenges through vocal health diagnosis. We leverage Qwen-Audio-Chat fine-tuned on three datasets collected in-situ from hospital patients, and present a multifaceted evaluation framework encompassing a safety assessment to mitigate diagnostic biases, cross-lingual performance analysis, and modality ablation studies. VocalAgent demonstrates superior accuracy on voice disorder classification compared to state-of-the-art baselines. Its LLM-based method offers a scalable solution for broader adoption of health diagnostics, while underscoring the importance of ethical and technical validation.