Graph neural networks (GNNs) and heterogeneous graph neural networks (HGNNs) are prominent techniques for homogeneous and heterogeneous graph representation learning, yet their performance in an end-to-end supervised framework greatly depends on the availability of task-specific supervision. To reduce the labeling cost, pre-training on self-supervised pretext tasks has become a popular paradigm,but there is often a gap between the pre-trained model and downstream tasks, stemming from the divergence in their objectives. To bridge the gap, prompt learning has risen as a promising direction especially in few-shot settings, without the need to fully fine-tune the pre-trained model. While there has been some early exploration of prompt-based learning on graphs, they primarily deal with homogeneous graphs, ignoring the heterogeneous graphs that are prevalent in downstream applications. In this paper, we propose HGPROMPT, a novel pre-training and prompting framework to unify not only pre-training and downstream tasks but also homogeneous and heterogeneous graphs via a dual-template design. Moreover, we propose dual-prompt in HGPROMPT to assist a downstream task in locating the most relevant prior to bridge the gaps caused by not only feature variations but also heterogeneity differences across tasks. Finally, we thoroughly evaluate and analyze HGPROMPT through extensive experiments on three public datasets.