We　investigate　a　Parker　problem　for　the　three-dimensional　compressible　isentropic　viscous　magnetohydrodynamic　system　with　zero　resistivity　in　the　presence　of　a　modified　gravitational　force　in　a　vertical　strip　domain　in　which　the　velocity　of　the　fluid　is　non-slip　on　the　boundary,　and　focus　on　the　stabilizing　effect　of　the　(equilibrium)　magnetic　field　through　the　non-slip　boundary　condition.　We　show　that　there　is　a　discriminant　Ξ　depending　on　the　known　physical　parameters,　for　the　stability/instability　of　the　Parker　problem.　More　precisely,　if　Ξ＞0,　then　the　Parker　problem　is　unstable,　i.e.,　the　Parker　instability　occurs,　while　if　Ξ＜0　and　the　initial　perturbation　satisfies　some　relations,　then　there　exists　a　global　(perturbation)　solution　which　decays　algebraically　to　zero　in　time,　i.e.,　the　Parker　instability　does　not　happen.　The　stability　results　in　this　paper　reveal　the　stabilizing　effect　of　the　magnetic　field　through　the　non-slip　boundary　condition　and　the　importance　of　boundary　conditions　upon　the　Parker　instability,　and　demonstrate　that　a　sufficiently　strong　magnetic　field　can　prevent　the　Parker　instability　from　occurring.　In　addition,　based　on　the　instability　results,　we　further　rigorously　verify　the　Parker　instability　under　Schwarzschild＇s　or　Tserkovnikov＇s　instability　conditions　in　the　sense　of　Hadamard　for　a　horizontally　periodic　domain.　©　2018　Elsevier　B.V.