Compared to sequential learning models, graph-based neural networks exhibit excellent ability in capturing global information and have been used for semi-supervised learning tasks. Most Graph Convolutional Networks are designed with the single-dimensional edge feature and failed to utilise the rich edge information about graphs. This paper introduces the ME-GCN (Multi-dimensional Edge-enhanced Graph Convolutional Networks) for semi-supervised text classification. A text graph for an entire corpus is firstly constructed to describe the undirected and multi-dimensional relationship of word-to-word, document-document, and word-to-document. The graph is initialised with corpus-trained multi-dimensional word and document node representation, and the relations are represented according to the distance of those words/documents nodes. Then, the generated graph is trained with ME-GCN, which considers the edge features as multi-stream signals, and each stream performs a separate graph convolutional operation. Our ME-GCN can integrate a rich source of graph edge information of the entire text corpus. The results have demonstrated that our proposed model has significantly outperformed the state-of-the-art methods across eight benchmark datasets.