It is proved the non-existence of Hopf hypersurfaces in $G_{2}({Bbb C}^{m+2})$, $m geq 3$, whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field
in the maximal quaternionic subbundle ${frak D}$ or its orthogonal complement ${frak D}^{bot}$ is invariant by the shape operator.
