With the proliferation of large language models (LLMs) in the medical domain, there is increasing demand for improved evaluation techniques to assess their capabilities. However, traditional metrics like F1 and ROUGE, which rely on token overlaps to measure quality, significantly overlook the importance of medical terminology. While human evaluation tends to be more reliable, it can be very costly and may as well suffer from inaccuracies due to limits in human expertise and motivation. Although there are some evaluation methods based on LLMs, their usability in the medical field is limited due to their proprietary nature or lack of expertise. To tackle these challenges, we present AutoMedEval, an open-sourced automatic evaluation model with 13B parameters specifically engineered to measure the question-answering proficiency of medical LLMs. The overarching objective of AutoMedEval is to assess the quality of responses produced by diverse models, aspiring to significantly reduce the dependence on human evaluation. Specifically, we propose a hierarchical training method involving curriculum instruction tuning and an iterative knowledge introspection mechanism, enabling AutoMedEval to acquire professional medical assessment capabilities with limited instructional data. Human evaluations indicate that AutoMedEval surpasses other baselines in terms of correlation with human judgments.