With the emergence of pretrained vision-language models (VLMs), considerable efforts have been devoted to fine-tuning them for downstream tasks. Despite the progress made in designing efficient fine-tuning methods, such methods require access to the model's parameters, which can be challenging as model owners often opt to provide their models as a black box to safeguard model ownership. This paper proposes a Collaborative Fine-Tuning (CraFT) approach for fine-tuning black-box VLMs to downstream tasks, where one only has access to the input prompts and the output predictions of the model. CraFT comprises two modules, a prompt generation module for learning text prompts and a prediction refinement module for enhancing output predictions in residual style. Additionally, we introduce an auxiliary prediction-consistent loss to promote consistent optimization across these modules. These modules are optimized by a novel collaborative training algorithm. Extensive experiments on few-shot classification over 15 datasets demonstrate the superiority of CraFT. The results show that CraFT achieves a decent gain of about 12% with 16-shot datasets and only 8,000 queries. Moreover, CraFT trains faster and uses only about 1/80 of the memory footprint for deployment, while sacrificing only 1.62% compared to the white-box method. Our code is publicly available at https://github.com/mrflogs/CraFT.