Abstract:  In this paper we discuss the quasilinear parabolic equationU■=▽(uu（1-u）β.Vu)+■（x,t.u）▽u+C（x,t,u）which is degenerate at u =0 and u=1.Let u（x,t）be a weak solution of the equation satisfying0<u（x,t）<1.Under some assumptions we establish H■lder continuity of u（x,t）.