Identifying structures in common forms the basis for networked systems design and optimization. However, real structures represented by graphs are often of varying sizes, leading to the low accuracy of traditional graph classification methods. These graphs are called cross-scale graphs. To overcome this limitation, in this study, we propose GSpect, an advanced spectral graph filtering model for cross-scale graph classification tasks. Compared with other methods, we use graph wavelet neural networks for the convolution layer of the model, which aggregates multi-scale messages to generate graph representations. We design a spectral-pooling layer which aggregates nodes to one node to reduce the cross-scale graphs to the same size. We collect and construct the cross-scale benchmark data set, MSG (Multi Scale Graphs). Experiments reveal that, on open data sets, GSpect improves the performance of classification accuracy by 1.62% on average, and for a maximum of 3.33% on PROTEINS. On MSG, GSpect improves the performance of classification accuracy by 15.55% on average. GSpect fills the gap in cross-scale graph classification studies and has potential to provide assistance in application research like diagnosis of brain disease by predicting the brain network's label and developing new drugs with molecular structures learned from their counterparts in other systems.