Spectral Graph Transducer(SGT) is one of the superior graph-based transductive learning methods for classification. As for the Spectral Graph Transducer algorithm, a good graph representation for data to be processed is very important. In this paper, we try to incorporate Latent Semantic Indexing(LSI) into SGT for text classification. Firstly, we exploit LSI to represent documents as vectors in a latent semantic space since we propose that the documents and their semantic relationships can be reflected more pertinently in this latent semantic space. Then, a graph needed by SGT is constructed. In the graph, a node corresponds to a vector from LSI. Finally, we apply the graph to Spectral Graph Transducer for text classification. The experiments gave us excellent results on both English and Chinese text classification datasets and demonstrated the validation of our assumption.