Graph Neural Networks (GNNs) have demonstrated remarkable efficacy in handling graph-structured data; however, they exhibit failures after deployment, which can cause severe consequences. Hence, conducting thorough testing before deployment becomes imperative to ensure the reliability of GNNs. However, thorough testing requires numerous manually annotated test data. To mitigate the annotation cost, strategically prioritizing and labeling high-quality unlabeled inputs for testing becomes crucial, which facilitates uncovering more model failures with a limited labeling budget. Unfortunately, existing test input prioritization techniques either overlook the valuable information contained in graph structures or are overly reliant on attributes extracted from the target model, i.e., model-aware attributes, whose quality can vary significantly. To address these issues, we propose a novel test input prioritization framework, named GraphRank, for GNNs. GraphRank introduces model-agnostic attributes to compensate for the limitations of the model-aware ones. It also leverages the graph structure information to aggregate attributes from neighboring nodes, thereby enhancing the model-aware and model-agnostic attributes. Furthermore, GraphRank combines the above attributes with a binary classifier, using it as a ranking model to prioritize inputs. This classifier undergoes iterative training, which enables it to learn from each round's feedback and improve its performance accordingly. Extensive experiments demonstrate GraphRank's superiority over existing techniques.