Graph　Neural　Networks　(GNNs)　have　emerged　as　a　crucial　deep　learning　framework　for　graph-structured　data.　However,　existing　GNNs　suffer　from　the　scalability　limitation,　which　hinders　their　practical　implementation　in　industrial　settings.　Many　scalable　GNNs　have　been　proposed　to　address　this　limitation.　However,　they　have　been　proven　to　act　as　low-pass　graph　filters,　which　discard　the　valuable　middle-　and　high-frequency　information.　This　paper　proposes　a　novel　graph　neural　network　named　Adaptive　Filtering　Graph　Neural　Networks　(AFGNN),　which　can　capture　all　frequency　information　on　large-scale　graphs.　AFGNN　consists　of　two　stages.　The　first　stage　utilizes　low-,　middle-,　and　high-pass　graph　filters　to　extract　comprehensive　frequency　information　without　introducing　additional　parameters.　This　computation　is　a　one-time　task　and　is　pre-computed　before　training,　ensuring　its　scalability.　The　second　stage　incorporates　a　node-level　attention-based　feature　combination,　enabling　the　generation　of　customized　graph　filters　for　each　node,　contrary　to　existing　spectral　GNNs　that　employ　uniform　graph　filters　for　the　entire　graph.　AFGNN　is　suitable　for　mini-batch　training,　and　can　enhance　scalability　and　efficiently　capture　all　frequency　information　from　large-scale　graphs.　We　evaluate　AFGNN　by　comparing　its　ability　to　capture　all　frequency　information　with　spectral　GNNs,　and　its　scalability　with　scalable　GNNs.　Experimental　results　illustrate　that　AFGNN　surpasses　both　scalable　GNNs　and　spectral　GNNs,　highlighting　its　superiority.　©　2023　Elsevier　Ltd