Multimodal large language models (LLMs) have achieved notable success across various domains, while research in the medical field has largely focused on unimodal images. Meanwhile, current general-domain multimodal models for videos still lack the capabilities to understand and engage in conversations about surgical videos. One major contributing factor is the absence of datasets in the surgical field. In this paper, we create a new dataset, Surg-QA, consisting of 102,000 surgical video-instruction pairs, the largest of its kind so far. To build such a dataset, we propose a novel two-stage question-answer generation pipeline with LLM to learn surgical knowledge in a structured manner from the publicly available surgical lecture videos. The pipeline breaks down the generation process into two stages to significantly reduce the task complexity, allowing us to use a more affordable, locally deployed open-source LLM than the premium paid LLM services. It also mitigates the risk of LLM hallucinations during question-answer generation, thereby enhancing the overall quality of the generated data. We further train LLaVA-Surg, a novel vision-language conversational assistant capable of answering open-ended questions about surgical videos, on this Surg-QA dataset, and conduct comprehensive evaluations on zero-shot surgical video question-answering tasks. We show that LLaVA-Surg significantly outperforms all previous general-domain models, demonstrating exceptional multimodal conversational skills in answering open-ended questions about surgical videos. We will release our code, model, and the instruction-tuning dataset.