Graph-based consistency principle has been successfully applied to many semi-supervised problems in machine learning. Its performance largely depends on the quality of augmented graphs, which has been recently proven that revealing graph properties and maintaining the invariance of graphs are crucial for good performance. However, existing topology- or feature-based augmentation methods are spectrally non-localized -- important spectrums are disturbed throughout the entire frequency range, and their invariance may not be well preserved. Efforts on this issue remain to be limited. This paper proposes a simple yet effective model called Localized SPectral AugmentatioN (LSPAN), which perturbs a concentrated part of graph spectrum with equivalent intensity using Fourier orthogonality, so as to enhance graph spectrum preservation as well as model prediction. Moreover, it also avoids the significant training time of inverse Fourier transform. Extensive empirical evaluation on real-world datasets clearly shows the performance gain of spectrally localized augmentation, as well as its good convergence and efficiency compared to existing graph methods.