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 \textbf{C}ollabo\textbf{ra}tive \textbf{F}ine-\textbf{T}uning (\textbf{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.