In　many　kinds　of　games　with　economic　significance,　it　is　very　important　to　study　the　submodularity　of　functions.　In　this　paper,　we　mainly　study　the　problem　of　maximizing　a　concave　function　over　an　intersection　of　two　matroids.　We　obtain　that　the　submodularity　may　not　be　preserved,　but　it　involves　one　maximal　submodular　problem　(or　minimal　supermodular　problem)　with　some　conditions.　Moreover,　we　also　present　examples　showing　that　these　conditions　can　be　satisfied.　©　2019,　Operations　Research　Society　of　China,　Periodicals　Agency　of　Shanghai　University,　Science　Press,　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.