Multivariate　time　series　classification　is　one　of　the　increasingly　important　issues　in　machine　learning.　Existing　methods　focus　on　establishing　the　global　long-range　dependencies　or　discovering　the　local　critical　sequence　fragments.　However,　they　often　ignore　the　combined　information　from　both　global　and　local　features.　In　this　paper,　we　propose　a　novel　network　(called　DA-Net)　based　on　dual　attention　to　mine　the　local–global　features　for　multivariate　time　series　classification.　Specifically,　DA-Net　consists　of　two　distinctive　layers,　i.e.,　the　Squeeze-Excitation　Window　Attention　(SEWA)　layer　and　the　Sparse　Self-Attention　within　Windows　(SSAW)　layer.　For　the　SEWA　layer,　we　capture　the　local　window-wise　information　by　explicitly　establishing　window　dependencies　to　prioritize　critical　windows.　For　the　SSAW　layer,　we　preserve　rich　activate　scores　with　less　computation　to　widen　the　window　scope　for　capturing　global　long-range　dependencies.　Based　on　the　two　elaborated　layers,　DA-Net　can　mine　critical　local　sequence　fragments　in　the　process　of　establishing　global　long-range　dependencies.　The　experimental　results　show　that　DA-Net　is　able　to　achieve　competing　performance　with　state-of-the-art　approaches　on　the　multivariate　time　series　classification.　©　2022　Elsevier　Inc.