In this paper we give a non-existence theorem for Hopf hypersurfaces M in complex two-plane Grassmannians $G_2(mathbb{C}^{m+2})$ whose normal Jacobi operator $ar{R}_N$ is parallel on the distribution F defined by $F=[{xi}]{cup}D^{ot}$, where [${xi}$] = Span{${xi}$}, $D^{ot}$ = Span {${xi}_1$, ${xi}_2$, ${xi}_3$} and $T_xM=D{oplus}D^{ot}$, $x{in}M$.