Hyper-relational knowledge graphs (KGs) contain additional key-value pairs, providing more information about the relations. In many scenarios, the same relation can have distinct key-value pairs, making the original triple fact more recognizable and specific. Prior studies on hyper-relational KGs have established a solid standard method for hyper-relational graph encoding. In this work, we propose a message-passing-based graph encoder with global relation structure awareness ability, which we call ReSaE. Compared to the prior state-of-the-art approach, ReSaE emphasizes the interaction of relations during message passing process and optimizes the readout structure for link prediction tasks. Overall, ReSaE gives a encoding solution for hyper-relational KGs and ensures stronger performance on downstream link prediction tasks. Our experiments demonstrate that ReSaE achieves state-of-the-art performance on multiple link prediction benchmarks. Furthermore, we also analyze the influence of different model structures on model performance.