Background Cancers are genetically heterogeneous, so anticancer drugs show varying degrees of effectiveness on patients due to their differing genetic profiles. Knowing patient’s responses to numerous cancer drugs are needed for personalized treatment for cancer. By using molecular profiles of cancer cell lines available from Cancer Cell Line Encyclopedia (CCLE) and anticancer drug responses available in the Genomics of Drug Sensitivity in Cancer (GDSC), we will build computational models to predict anticancer drug responses from molecular features. Results We propose a novel deep neural network model that integrates multi-omics data available as gene expressions, copy number variations, gene mutations, reverse phase protein array expressions, and metabolomics expressions, in order to predict cellular responses to known anti-cancer drugs. We employ a novel graph embedding layer that incorporates interactome data as prior information for prediction. Moreover, we propose a novel attention layer that effectively combines different omics features, taking their interactions into account. The network outperformed feedforward neural networks and reported 0.90 for $$R^2$$ R 2 values for prediction of drug responses from cancer cell lines data available in CCLE and GDSC. Conclusion The outstanding results of our experiments demonstrate that the proposed method is capable of capturing the interactions of genes and proteins, and integrating multi-omics features effectively. Furthermore, both the results of ablation studies and the investigations of the attention layer imply that gene mutation has a greater influence on the prediction of drug responses than other omics data types. Therefore, we conclude that our approach can not only predict the anti-cancer drug response precisely but also provides insights into reaction mechanisms of cancer cell lines and drugs as well.