We prove that any n n -dimensional closed mean convex λ \lambda - hypersurface is convex if λ ≤ 0. \lambda \le 0. This generalizes Guang’s work on 2 2 -dimensional strictly mean convex λ \lambda -hypersurfaces. As a corollary, we obtain a gap theorem for closed λ \lambda -hypersurfaces with λ ≤ 0. \lambda \le 0.