The　global　existence　of　small　smooth　solutions　to　the　equations　of　two-dimensional　incompressible,　inviscid,　nonresistive　magnetohydrodynamic　(MHD)　fluids　with　velocity　damping　has　been　established　in　[J.　H.　Wu,　Y.　F.　Wu,　and　X.　J.　Xu,　SIAM　J.　Math.　Anal.,　47　(2015),　pp.　2630–2656].　In　this　paper　we　further　study　the　global　existence　for　an　initial-boundary　value　problem　in　a　horizontally　periodic　domain　with　finite　height　in　three　dimensions.　Motivated　by　the　multilayer　energy　method　introduced　in　[Y.　Guo　and　I.　Tice,　Arch.　Ration.　Mech.　Anal.,　207　(2013),　pp.　459–531],　we　develop　a　new　type　of　two-layer　energy　structure　to　overcome　the　difficulties　arising　from　three-dimensional　nonlinear　terms　in　the　MHD　equations,　and　prove　thus　the　initial-boundary　value　problem　admits　a　unique　global　smooth　solution　with　small　initial　data.　Moreover,　the　solution　decays　exponentially　in　time　to　some　rest　state.　Our　two-layer　energy　structure　enjoys　two　features:　(1)　the　lower-order　energy　(functional)　cannot　be　controlled　by　the　higher-order　energy;　(2)　under　the　a　priori　smallness　assumption　of　the　lower-order　energy,　we　can　first　close　the　higher-order　energy　estimates,　and　then　further　close　the　lower-energy　estimates　in　turn.　©　2022　Society　for　Industrial　and　Applied　Mathematics.