In　this　paper,　we　study　orbital　stability　of　peakons　for　the　generalized　modified　Camassa-Holm　(gmCH)　equation,　which　is　a　natural　higher-order　generalization　of　the　modified　Camassa-Holm　(mCH)　equation,　and　admits　Hamiltonian　form　and　single　peakons.　We　first　show　that　the　single　peakon　is　the　usual　weak　solution　of　the　PDEs.　Some　sign　invariant　properties　and　conserved　densities　are　presented.　Next,　by　constructing　the　corresponding　auxiliary　function　h(t,　x)　and　establishing　a　delicate　polynomial　inequality　relating　to　the　two　conserved　densities　with　the　maximal　value　of　approximate　solutions,　the　orbital　stability　of　single　peakon　of　the　gmCH　equation　is　verified.　We　introduce　a　new　approach　to　prove　the　key　inequality,　which　is　different　from　that　used　for　the　mCH　equation.　This　extends　the　result　on　the　stability　of　peakons　for　the　mCH　equation　(Qu　et　al.　2013)　[36]　successfully　to　the　higher-order　case,　and　is　helpful　to　understand　how　higher-order　nonlinearities　affect　the　dispersion　dynamics.　(C)　2018　Elsevier　Inc.　All　rights　reserved.