Large Vision-Language Models (LVLMs) have shown significant potential in assisting medical diagnosis by leveraging extensive biomedical datasets. However, the advancement of medical image understanding and reasoning critically depends on building high-quality visual instruction data, which is costly and labor-intensive to obtain, particularly in the medical domain. To mitigate this data-starving issue, we introduce Self-Training Large Language and Vision Assistant for Medical (STLLaVA-Med). The proposed method is designed to train a policy model (an LVLM) capable of auto-generating medical visual instruction data to improve data efficiency, guided through Direct Preference Optimization (DPO). Specifically, a more powerful and larger LVLM (e.g., GPT-4o) is involved as a biomedical expert to oversee the DPO fine-tuning process on the auto-generated data, encouraging the policy model to align efficiently with human preferences. We validate the efficacy and data efficiency of STLLaVA-Med across three major medical Visual Question Answering (VQA) benchmarks, demonstrating competitive zero-shot performance with the utilization of only 9% of the medical data.