Spatio-temporal　neural　networks　have　been　successfully　applied　to　weather　forecasting　tasks　recently.　The　key　notion　is　to　learn　spatio-temporal　features　concurrently　from　spatial　and　temporal　dependencies.　Existing　methods　are　mainly　based　on　local　smoothness　assumptions　where　the　features　are　learned　by　accumulating　information　in　local　spatio-temporal　regions.　However,　the　weather　conditions　in　a　certain　spatio-temporal　region　are　usually　influenced　by　global　meteorological　changes　and　long-range　historical　weather　conditions.　Therefore,　these　methods　that　ignore　the　large-scale　spatio-temporal　effects　can　hardly　learn　effective　features.　In　this　paper,　we　propose　a　novel　spatio-temporal　Transformer　network　in　weather　forecasting　to　address　the　above　challenges.　The　main　idea　is　to　leverage　the　Transformer　architecture　to　carefully　capture　the　multi-scale　spatial　and　long-range　temporal　information　in　weather　data.　First,　we　propose　to　combine　the　global　and　local　position　encodings　based　on　absolute　geographic　locations　and　relative　geodesic　distances　and　insert　them　into　the　spatial　Transformer　to　extract　the　multi-scale　spatial　information　in　meteorological　graphs.　Then,　we　further　capture　the　long-range　temporal　dependencies　by　a　temporal　Transformer　where　the　attention　mechanism　is　used　to　improve　the　representation　ability　and　scalability　of　the　models.　Extensive　experiments　over　real　weather　datasets　demonstrate　the　effectiveness　of　our　framework.　IEEE