Magnetostriction-based　electromagnetic　acoustic　transducer　(M-EMAT)　is　a　promising　tool　for　generating　fundamental　shear-horizontal　(SH0)　mode　guided　waves　in　plate.　Though　the　M-EMAT　possesses　high-order　harmonics　excitation　ability　in　nature,　its　conventional　way　can　only　generate　a　fundamental　component　of　SH0　mode.　The　analytical　modeling　was　performed　in　this　study　to　releasing　the　ability　of　M-EMAT　in　generating　odd　harmonics　of　SH0　mode.　First,　the　inaccurate　conditions　of　magnetic　fields　for　relative　permeability　calculation　in　the　existing　model　are　corrected　in　the　proposed　model.　Second,　the　error　of　the　existing　model　in　predicting　the　spectrum　of　the　SH0　mode　generated　in　Nickel　plate　is　estimated.　Third,　numerical　solutions　are　provided　by　the　improved　model　to　examine　the　key　factors　governing　the　ability　of　M-EMAT　in　generating　odd　harmonics　of　SH0　mode.　The　conclusions　demonstrated　that　the　intensity　ratio　(H-S/H-D)　of　static　and　dynamic　magnetic　fields　is　adjusted　below　1　and　the　ability　of　M-EMAT　in　generating　odd　harmonics　of　SH0　mode　can　be　activated.　The　normalized　amplitude　of　3rd　harmonics　decays　exponentially　with　the　increase　of　H-S/H-D,　which　is　independent　of　geometrical　parameters　of　M-EMAT.　The　improved　model　can　effectively　optimize　excitation　parameters　of　M-EMAT　and　generate　odd　harmonics　of　SH0　mode　in　plate.