  There are several kinds of classification problems for real hypersurfaces in
complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh
classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb
parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce a
new notion of generalized Tanaka-Webster Reeb parallel Ricci tensor for $M$ in
$G_2({\mathbb C}^{m+2})$. By using such parallel conditions, we give complete
classifications of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$.
