The generalized E-convex function plays an important role in the optimization theory. The relationship between generalized E-convex function and convex function is obtained by comparing the correlation properties of convex functions. Then a counterexample is given for the proof of the lemma in the literature ［5］, and the equivalence between the E-convex function and the E-monotone is proved newly. It is further proved that f has an upper bound on a specific open set E(M) in a finite dimensional space. Finally, the properties and conclusions of the generalized E-convex function are generalized.