Power　system　state　estimation　is　a　primary　and　major　method　for　monitoring　power　grids　in　real　time.　Massive　synchrophasor　data　contains　temporal　correlations　and　spatial　characteristics　based　on　the　physical　constraints　of　the　power　system.　The　spectral-domain　convolution　method　based　on　the　graph　Fourier　transform　is　used　to　construct　a　multilayer　graph　convolution　neural　network　model　to　predict　the　short-term　states　of　a　power　system,　including　the　latest　state,　when　the　power　system　is　in　the　quasi-steady　state.　Combining　the　advantages　of　linear　state　estimation,　a　forecasting-aided　state　estimation　method　that　can　take　advantage　of　predicted　values　and　phase　measurement　units　is　designed　to　obtain　the　real-time　state.　Furthermore,　predicted　innovations　analysis　method　are　proposed　to　identify　system　mutations　and　bad　data.　Enough　simulation　tests　validate　that　the　proposed　method　can　accurately　estimate　the　real-time　state　of　a　power　system.