This　paper　concerns　the　free-surface　problem　of　incompressible　ideal　MHD　fluids　with　velocity　damping　in　a　two-dimensional　(2D)　horizontally　periodic　slab　domain　impressed　by　a　uniform　horizontal　magnetic　field.　We　prove　that　the　problem　is　globally　well-posed　for　the　small　initial　data　and　the　solution　decays　exponentially　in　time　to　the　equilibrium,　where　both　the　Taylor　sign　condition　and　the　surface　tension　are　not　required　in　this　paper　due　to　the　stabilizing　effect　of　horizontal　magnetic　field.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Switzerland　AG　2024.