Strain　glass　is　a　frozen　disordered　strain　state　with　local　strain　order　manifested　by　nano-sized　strain　domains,　which　is　formed　as　a　result　of　doping　sufficient　point　defects　into　the　normal　martensitic　system.　Exploration　of　the　transition　between　strain　glass　and　long-range　strain-ordered　martensite　is　of　both　great　fundamental　importance　and　practical　interest.　However,　it　remains　a　mystery　whether　magnetic　field　can　induce　a　transition　from　strain　glass　to　martensite.　Here,　we　report　for　the　first　time　the　magnetic-field-induced　strain-glass-to-martensite　transition,　in　a　model　system　Fe-Mn-Ga.　It　was　found　that　the　martensitic　transformation　temperature　of　the　Fe43-xMn28Ga29+x,　alloys　decreases　rapidly　with　increasing　x　and　the　martensitic　transformation　disappears　when　x　reaches　the　critical　value　x(c)　=2.0.　Strain　glass　transition　occurs　in　the　alloy　with　x　=　2.0　(Fe41Mn28Ga31),　which　is　confirmed　by　the　invariance　of　the　average　structure　during　cooling,　the　frequency　dispersion　of　the　ac　storage　modulus　and　internal　friction　following　the　Vogel-Fulcher　relation,　and　the　formation　of　nanodomains.　The　magnetic-field-induced　transition　from　strain　glass　to　non-modulated　tetragonal　martensite　in　Fe41Mn28Ga31,　was　indicated　by　the　abrupt　magnetization　jump　on　the　M(H)　curve　and　directly　evidenced　by　the　crystal　structure　evolution　with　magnetic　field　change　revealed　by　in-situ　neutron　diffraction　experiments.　The　microscopic　mechanism　for　this　magnetic-field-induced　strain-glass-to-martensite　transition　is　discussed.　The　present　study　may　not　only　help　establish　the　unified　theory　for　strain-glass-to-martensite　transition　under　external　fields　but　also　open　a　new　avenue　for　designing　advanced　materials　with　novel　functional　properties.　(C)　2019　Acta　Materialia　Inc.　Published　by　Elsevier　Ltd.　All　rights　reserved.