The knowledge graph is a structure to store and represent knowledge, and recent studies have discussed its capability to assist language models for various applications. Some variations of knowledge graphs aim to record arguments and their relations for computational argumentation tasks. However, many must simplify semantic types to fit specific schemas, thus losing flexibility and expression ability. In this paper, we propose the **Hi**erarchical **Ar**gumentation **G**raph (Hi-ArG), a new structure to organize arguments. We also introduce two approaches to exploit Hi-ArG, including a text-graph multi-modal model GreaseArG and a new pre-training framework augmented with graph information. Experiments on two argumentation tasks have shown that after further pre-training and fine-tuning, GreaseArG supersedes same-scale language models on these tasks, while incorporating graph information during further pre-training can also improve the performance of vanilla language models. Code for this paper is available at <https://github.com/ljcleo/Hi-ArG>.