In　this　paper,　we　solve　the　problem　of　feature　matching　by　designing　an　end-to-end　network　(called　TSSN-Net).　Given　putative　correspondences　of　feature　points　in　two　views,　existing　deep　learning　based　methods　formulate　the　feature　matching　problem　as　a　binary　classification　problem.　In　these　methods,　a　normalizer　plays　an　important　role　in　the　networks.　However,　they　adopt　the　same　normalizer　in　all　normalization　layers　of　the　entire　networks,　which　will　result　in　suboptimal　performance.　To　address　this　problem,　we　propose　a　Two-step　Sparse　Switchable　Normalization　Block,　which　involves　the　advantage　of　adaptive　normalization　for　different　convolution　layers　from　Sparse　Switchable　Normalization　and　robust　global　context　information　from　Context　Normalization.　Moreover,　to　capture　local　information　of　correspondences,　we　propose　a　Multi-Scale　Correspondence　Grouping　algorithm,　by　defining　a　multi-scale　neighborhood　representation,　to　search　for　consistent　neighbors　of　each　correspondence.　Finally,　with　a　series　of　convolution　layers,　the　end-to-end　TSSN-Net　is　proposed　to　learn　correspondences　with　heavy　outliers　for　feature　matching.　Our　experimental　results　have　shown　that　our　network　achieves　the　state-of-the-art　performance　on　benchmark　datasets.　©　2021　Elsevier　B.V.