Current video summarization methods primarily depend on supervised computer vision techniques, which demands time-consuming manual annotations. Further, the annotations are always subjective which make this task more challenging. To address these issues, we analyzed the feasibility in transforming the video summarization into a text summary task and leverage Large Language Models (LLMs) to boost video summarization. This paper proposes a novel self-supervised framework for video summarization guided by LLMs. Our method begins by generating captions for video frames, which are then synthesized into text summaries by LLMs. Subsequently, we measure semantic distance between the frame captions and the text summary. It's worth noting that we propose a novel loss function to optimize our model according to the diversity of the video. Finally, the summarized video can be generated by selecting the frames whose captions are similar with the text summary. Our model achieves competitive results against other state-of-the-art methods and paves a novel pathway in video summarization.