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GNN-based methods have achieved excellent results as a mainstream task in drug response prediction tasks in recent years. Traditional GNN methods use only the atoms in a drug molecule as nodes to obtain the representation of the molecular graph through node information passing, whereas the method using the transformer can only extract information about the nodes. However, the covalent bonding and chirality of a drug molecule have a great influence on the pharmacological properties of the molecule, and these information are implied in the chemical bonds formed by the edges between the atoms. In addition, CNN methods for modelling cell lines genomics sequences can only perceive local rather than global information about the sequence. In order to solve the above problems, we propose the decoupled dual transformer structure with edge embedded for drug respond prediction (TransEDRP), which is used for the representation of cell line genomics and drug respectively. For the drug branch, we encoded the chemical bond information within the molecule as the embedding of the edge in the molecular graph, extracted the global structural and biochemical information of the drug molecule using graph transformer. For the branch of cell lines genomics, we use the multi-headed attention mechanism to globally represent the genomics sequence. Finally, the drug and genomics branches are fused to predict IC50 values through the transformer layer and the fully connected layer, which two branches are different modalities. Extensive experiments have shown that our method is better than the current mainstream approach in all evaluation indicators.