Many powerful computational methods based on graph neural networks (GNNs) have been proposed to predict drug-protein interactions (DPIs). It can effectively reduce laboratory workload and the cost of drug discovery and drug repurposing. However, many clinical functions of drugs and proteins are unknown due to their unobserved indications. Therefore, it is difficult to establish a reliable drug-protein heterogeneous network that can describe the relationships between drugs and proteins based on the available information. To solve this problem, we propose a DPI prediction method that can self-adaptively adjust the topological structure of the heterogeneous networks, and name it SATS. SATS establishes a representation learning module based on graph attention network to carry out the drug-protein heterogeneous network. It can self-adaptively learn the relationships among the nodes based on their attributes and adjust the topological structure of the network according to the training loss of the model. Finally, SATS predicts the interaction propensity between drugs and proteins based on their embeddings. The experimental results show that SATS can effectively improve the topological structure of the network. The performance of SATS outperforms several state-of-the-art DPI prediction methods under various evaluation metrics. These prove that SATS is useful to deal with incomplete data and unreliable networks. The case studies on the top section of the prediction results further demonstrate that SATS is powerful for discovering novel DPIs.