Inspired by the success of vision-language methods (VLMs) in zero-shot classification, recent works attempt to extend this line of work into object detection by leveraging the localization ability of pretrained VLMs and generating pseudolabels for unseen classes in a self-training manner. However, since the current VLMs are usually pretrained with aligning sentence embedding with global image embedding, the direct use of them lacks fine-grained alignment for object instances, which is the core of detection. In this article, we propose a simple but effective fine-grained visual-text prompt-driven self-training paradigm for open-vocabulary detection (VTP-OVD) that introduces a fine-grained visual-text prompt adapting stage to enhance the current self-training paradigm with a more powerful fine-grained alignment. During the adapting stage, we enable VLM to obtain fine-grained alignment using learnable text prompts to resolve an auxiliary dense pixelwise prediction task. Furthermore, we propose a visual prompt module to provide the prior task information (i.e., the categories need to be predicted) for the vision branch to better adapt the pretrained VLM to the downstream tasks. Experiments show that our method achieves the state-of-the-art performance for open-vocabulary object detection, e.g., 31.5% mAP on unseen classes of COCO.