To evaluate Large Language Models (LLMs) for question answering (QA), traditional methods typically focus on assessing single-turn responses to given questions. However, this approach doesn't capture the dynamic nature of human-AI interactions, where humans actively seek information through conversation. Recent works in human-computer interaction (HCI) have employed human evaluators to conduct interactions and evaluations, but they are often prohibitively expensive and time-consuming to scale. We introduce an automatic evaluation framework IQA-EVAL to achieve Interactive Question Answering Evaluations, more specifically, we introduce a LLM-based Evaluation Agent (LEA) that can: (1) simulate human behaviors to generate interactions with IQA models; (2) automatically evaluate the generated interactions. Moreover, we propose assigning personas to LEAs to better simulate groups of real human evaluators. We show that: (1) our evaluation framework with GPT-4 (or Claude) as the backbone model achieves a high correlation with human evaluations on the IQA task; (2) assigning personas to LEA to better represent the crowd further significantly improves correlations. Finally, we use our automatic metric to evaluate five recent representative LLMs with over 1000 questions from complex and ambiguous question answering tasks, which comes with a substantial cost of $5k if evaluated by humans.