Generalized convex function is a generalization of convex func-tion,including pseudoconvex function,quasiconvex function,r-convex function,etc.The properties and operation properties of generalized convex functionplay an imporant role in generalized convex programming.Xue Jiasheng discu-sed the constructive method of pseudoconvex function;J.P.Crouzeix dicussedthe properties of quasiconvex function.This paper only discusses a class ofgeneralized convex function,r-convex functions.