In Visually-rich Document Understanding (VrDU), recent advances of incorporating layout and image features into the pre-training language models have achieved significant progress. Existing methods usually developed complicated dedicated architectures based on pre-trained models and fine-tuned them with costly high-quality data to eliminate the inconsistency of knowledge distribution between the pre-training task and specialized downstream tasks. However, due to their huge data demands, these methods are not suitable for few-shot settings, which are essential for quick applications with limited resources but few previous works are presented. To solve these problems, we propose a unified Knowledge-aware prompt-tuning framework for Visual-rich Document Understanding (KnowVrDU) to enable broad utilization for diverse concrete applications and reduce data requirements. To model heterogeneous VrDU structures without designing task-specific architectures, we propose to reformulate various VrDU tasks into a single question-answering format with task-specific prompts and train the pre-trained model with the parameter-efficient prompt tuning method. To bridge the knowledge gap between the pre-training task and specialized VrDU tasks without additional annotations, we propose a prompt knowledge integration mechanism to leverage external open-source knowledge bases. We conduct experiments on several benchmark datasets in few-shot settings and the results validate the effectiveness of our method.