Air　quality　prediction　utilizes　IoT　technologies　to　collect　data　centrally　for　model　training,　which　may　cause　regulatory　risks,　privacy　concerns,　and　high　costs　of　integrating　data.　Meanwhile,　distributed　training　through　federated　learning　relies　on　the　pre-defined　graph　structure　generated　by　the　geographic　locations　of　air　monitoring　stations,　which　fails　to　capture　the　potential　spatial　relationships　between　air　monitoring　stations.　In　addition,　the　inherent　multi-period　attribute　of　air　quality　data　makes　time　series　changes　extremely　complex.　To　this　end,　this　paper　proposes　a　Federated　framework　for　air　quality　prediction　with　Pre-defined　graph　and　Adaptive　Graph　(FedPAG).　Specifically,　the　client　encodes　the　air　quality　data　and　meteorological　data　provided　by　the　Internet　of　Things　(IoT)　system　using　the　multi-period　interaction　and　encoder　modules　to　capture　the　proximity　and　periodicity　features　of　the　time　series　data.　Next,　the　server　combines　the　hidden　states　uploaded　by　the　clients　with　pre-defined　graph　and　adaptive　graph　respectively　and　forms　node　embeddings　to　capture　the　spatial　features　among　the　clients.　Then,　the　client　concatenates　the　hidden　states　with　node　embeddings　to　fuse　the　spatial　information　and　feeds　them　into　the　decoder　to　obtain　the　final　predicted　values.　Finally,　we　conduct　experiments　on　the　Beijing　and　Shijiazhuang　datasets　to　demonstrate　the　effectiveness　of　the　proposed　method.　©　2014　IEEE.