Finding new uses for current drugs can be accomplished with the help of computational drug repositioning. Many deep learning-based techniques have been developed recently to find possible drug-disease associations (DDAs). However, effectively utilizing the connections between biological elements to capture biological interactions to improve DDAs prediction is still a difficult task. To address the above issues, we propose a hybrid graph representation learning method (i.e., GTDDA). Specifically, we replace the self-attention mechanism in the Transformer with graph attention layer and design a new graph Transformer encoder (i.e., GATT) for generating graph embedding. First, drug-drug and disease-disease similarity networks are used to construct the graphs. Secondly, a hybrid graph embedding model is shown to train features for drugs and diseases sequentially at the same time, by combining graph convolutional network (GCN) with GATT. Lastly, predictive models that identify DDAs are constructed by concatenating the learnt features. A series of experiment results show that GTDDA outperforms several advanced DDAs prediction methods, which can provide effective predictions for the discovery of new indications for drugs and new treatments for diseases.