The computational prediction of mass spectra is a vital approach for identifying small-molecule structures. Existing methods have adopted approaches such as rule-based frameworks and deep learning models to predict mass spectra from molecular structures. However, due to the complex structure of molecules and the intricate fragmentation patterns in mass spectra, it is still challenging to effectively utilize the local and global features for modeling molecular fragmentation. The local features of molecules are vital for capturing the fine-grained structural details, while the global features are essential for understanding the complex interactions between substructures. In this work, we propose GraphMS, a novel model that integrates local and global graph features for mass spectral prediction. We first decompose the molecular graph into chemically meaningful substructures for extracting local features. A Transformer module is then applied to capture global features and model long-range dependencies between super nodes. Finally, the local and global features are fused adaptively to create a comprehensive molecular representation for mass spectrum prediction. Experiments on multiple datasets demonstrate that GraphMS outperforms existing methods, achieving higher accuracy and better generalization in mass spectrum prediction.