Motivation Drug response prediction (DRP) plays an important role in precision medicine (e.g., for cancer analysis and treatment). Recent advances in deep learning algorithms make it possible to predict drug responses accurately based on genetic profiles. However, existing methods ignore the potential relationships among genes. In addition, similarity among cell lines/drugs was rarely considered explicitly. Results We propose a novel DRP framework, called TGSA, to make better use of prior domain knowledge. TGSA consists of Twin Graph neural networks for Drug Response Prediction (TGDRP) and a Similarity Augmentation (SA) module to fuse fine-grained and coarse-grained information. Specifically, TGDRP abstracts cell lines as graphs based on STRING protein-protein association networks and employs Graph Neural Networks (GNNs) for representation learning. SA views DRP as an edge regression problem on a heterogeneous graph and utilizes GNNs to smooth the representations of similar cell lines/drugs. Besides, we introduce an auxiliary pre-training strategy to remedy the identified limitations of scarce data and poor out-of-distribution generalization. Extensive experiments on the GDSC2 dataset demonstrate that our TGSA consistently outperforms all the state-of-the-art baselines under various experimental settings. We further evaluate the effectiveness and contributions of each component of TGSA via ablation experiments. The promising performance of TGSA shows enormous potential for clinical applications in precision medicine. Availability The source code is available at https://github.com/violet-sto/TGSA. Supplementary information Supplementary data are available at Bioinformatics online.