Detecting Schelling Points—salient 3D mesh landmarks that serve as natural reference points for shape analysis—is a challenging problem in geometry processing. While existing CNN-based methods struggle with limited receptive fields and poor geometric context modeling, this paper proposes {\em SchellingFormer}, a novel Laplacian matrix-guided Geometric Transformer that effectively captures long-range dependencies and discriminative geometric features for robust Schelling point prediction. Our framework consists of two key components: (i) a hybrid geometric feature embedding module that integrates handcrafted descriptors (coordinates, Gaussian curvature, and curvature differences) to encode local geometry, and (ii) a Laplacian-driven vector attention mechanism, where spatial relationships encoded by the Laplacian matrix guide feature aggregation with the Transformer. This approach enables adaptive, geometry-aware message passing and contextual representation learning. Extensive experiments demonstrate that SchellingFormer outperforms state-of-the-art methods across multiple evaluation metrics. Our work bridges the gap between spectral mesh analysis and Transformer-based learning, offering a powerful tool for 3D shape understanding tasks such as shape matching and saliency detection.