Graph　Neural　Networks　(GNNs)　are　widely　used　on　a　variety　of　graph-based　machine　learning　tasks.　For　node-level　tasks,　GNNs　have　strong　power　to　model　the　homophily　property　of　graphs　(i.e.,　connected　nodes　are　more　similar),　while　their　ability　to　capture　heterophily　property　is　often　doubtful.　This　is　partially　caused　by　the　design　of　the　feature　transformation　with　the　same　kernel　for　the　nodes　in　the　same　hop　and　the　followed　aggregation　operator.　One　kernel　cannot　model　the　similarity　and　the　dissimilarity　(i.e.,　the　positive　and　negative　correlation)　between　node　features　simultaneously　even　though　we　use　attention　mechanisms　like　Graph　Attention　Network　(GAT),　since　the　weight　calculated　by　attention　is　always　a　positive　value.　In　this　paper,　we　propose　a　novel　GNN　model　based　on　a　bi-kernel　feature　transformation　and　a　selection　gate.　Two　kernels　capture　homophily　and　heterophily　information　respectively,　and　the　gate　is　introduced　to　select　which　kernel　we　should　use　for　the　given　node　pairs.　We　conduct　extensive　experiments　on　various　datasets　with　different　homophily-heterophily　properties.　The　experimental　results　show　consistent　and　significant　improvements　against　state-of-the-art　GNN　methods.