In complex two-plane Grassmannians G 2 (C m+2) = SU 2+m /S(U 2 ·U m), it is known that a real hyper-surface satisfying the condition (ˆ L (k) ξ R ξ)Y = (L ξ R ξ)Y is locally congruent to an open part of a tube around a totally geodesic G 2 (C m+1) in G 2 (C m+2). In this paper, as an abient space, we consider a complex hyperbolic two-plane Grassmannian SU 2,m /S(U 2 ·U m) and give a complete classification of Hopf real hypersurfaces in SU 2,m /S(U 2 ·U m) with the above condition.