Short text classification task is a special kind of text classification task in that the text to be classified is generally short, typically generating a sparse text representation that lacks rich semantic information. Given this shortcoming, scholars worldwide have explored improved short text classification methods based on deep learning. However, existing methods cannot effectively use concept knowledge and long-distance word dependencies. Therefore, based on graph neural networks from the perspective of text composition, we propose concept and dependencies enhanced graph convolutional networks for short text classification. First, the co-occurrence relationship between words, the inclusion relationship between documents and words, long-distance word dependencies, and the association relationship between external concepts and words are defined. Then, a text graph is constructed for an entire text corpus based on the four relationships. Finally, the text graph is input into graph convolutional neural networks, and the category of each document node is predicted after two layers of convolution. Experimental results show that our proposed method overall best on multiple classical English text classification datasets.