With growing applications in safety-critical domains such as autonomous vehicles and healthcare systems, graph neural networks (GNNs) are expected to provide predictions that are not only accurate but also reliable. Confidence calibration is a crucial task closely related to improve the reliability of machine learning models. Current GNN calibration methods primarily address challenges arising from the non-Euclidean topology structure of graph data and a general trend of under-confidence. However, our empirical studies have shown that these methods often fail to deal with local miscalibrations where community homophily diverges from global ones, such as high-homophily nodes in heterophilous graphs. To tackle this issue, we introduce Adaptive Spectral Temperature Scaling (ASTS), a novel spectral-based calibration method tailored for graphs with varying levels of homophily. On top of the node-wise temperature scaling framework, ASTS incorporates two components: (1) dual-channel graph filters that adaptively integrate similar and dissimilar information from neighborhood, (2) an innovative adaptive edge dropout module that alleviates issues induced by low-degree nodes. These designs ensure that ASTS is structure-aware, global trend-aware and well-adapted to different graph structures. Our extensive empirical studies confirm ASTS’s superior calibration performance over existing methods across graphs of diverse homophily ratios.