We propose a novel and challenging benchmark, AutoEval-Video, to comprehensively evaluate large vision-language models in open-ended video question answering. The comprehensiveness of AutoEval-Video is demonstrated in two aspects: 1) AutoEval-Video constructs open-ended video-questions across 9 skill dimensions, addressing capabilities of perception, comprehension, and generation. 2) AutoEval-Video contains newly collected videos that cover over 40 distinct themes. To efficiently evaluate responses to the open-ended questions, we employ an LLM-based evaluation approach, but instead of merely providing a reference answer, we annotate unique evaluation rules for every single instance (video-question pair). To maximize the robustness of these rules, we develop a novel adversarial annotation mechanism. By using instance-specific rules as prompt, GPT-4, as an automatic evaluator, can achieve a stable evaluation accuracy of around 97.0%, comparable to the 94.9% - 97.5% accuracy of a human evaluator. Furthermore, we assess the performance of eight large vision-language models on AutoEval-Video. Among them, GPT-4V(ision) significantly outperforms other models, achieving an accuracy of 32.2%. However, there is still substantial room for improvement compared to human accuracy of 72.8%. By conducting an extensive case study, we uncover several drawbacks of GPT-4V, such as limited temporal and dynamic comprehension, and overly general responses.