Short text classification is an important research problem of Natural Language Processing （NLP）， and is widely used in news classification， sentiment analysis， comment analysis and other fields. Aiming at the problem of data sparsity in short text classification， by introducing node and edge weight features of corpora， based on Graph ATtention network （GAT）， a new graph attention network named Node-Edge GAT （NE-GAT） by fusing node and edge weight features was proposed. Firstly， a heterogeneous graph was constructed for each corpus， Gravity Model （GM） was used to evaluate the importance of word nodes， and edge weights were obtained through Point Mutual Information （PMI） between nodes. Secondly， a text-level graph was constructed for each sentence， node importance and edge weights were integrated into the update process of nodes. Experimental results show that， the average accuracy of the proposed model on the test sets reaches 75.48%， which is better than those of the models such as Text Graph Convolution Network （Text-GCN）， Text-Level-Graph Neural Network （TL-GNN） and Text classification method for INductive word representations via Graph neural networks （Text-ING）. Compared with original GAT， the proposed model has the average accuracy improved by 2.32 percentage points， which verifies the effectiveness of the proposed model.