In　this　paper,　we　consider　the　variable-order　nonlinear　fractional　diffusion　equation　partial　derivative　u(x,　t)/partial　derivative　t　=　B(x,　t)(x)R(alpha(x,　t))u(x,　t)　+　f　(u,　x,　t),　where　R-x(alpha(x,t))　is　a　generalized　Riesz　fractional　derivative　of　variable　order　alpha(x,　t)　(1　＜　alpha(x,　t)　＜=　2)　and　the　nonlinear　reaction　term　f　(u,　x,　t)　satisfies　the　Lipschitz　condition　vertical　bar　f(u(1),　x,　t)　-　f(u(2),　x,　t)vertical　bar　＜=　L　vertical　bar　u(1)　-　u(2)vertical　bar.　A　new　explicit　finite-difference　approximation　is　introduced.　The　convergence　and　stability　of　this　approximation　are　proved.　Finally,　some　numerical　examples　are　provided　to　show　that　this　method　is　computationally　efficient.　The　proposed　method　and　techniques　are　applicable　to　other　variable-order　nonlinear　fractional　differential　equations.　Crown　Copyright　(C)　2009　Published　by　Elsevier　Inc.　All　rights　reserved.