  We study charmless pure annihilation type radiative B decays within the QCD
factorization approach. After adding the vertex corrections to the naive
factorization approach, we find that the branching ratios of
$\bar{B}^0_d\to\phi\gamma$, $\bar{B}^0_s\to\rho^0\gamma$ and
$\bar{B}^0_s\to\omega\gamma$ within the standard model are at the order of
$\mathcal{O}(10^{-12})$, $\mathcal{O}(10^{-10})$ and $\mathcal{O}(10^{-11})$,
respectively. The smallness of these decays in the standard model makes them
sensitive probes of flavor physics beyond the standard model. To explore their
physics potential, we have estimated the contribution of $Z^\prime$ boson in
the decays. Within the allowed parameter space, the branching ratios of these
decay modes can be enhanced remarkably in the non-universal $Z^\prime$ model:
The branching ratios can reach to $\mathcal{O}(10^{-8})$ for $\bar B_s^0 \to
\rho^0(\omega)\gamma$ and $\mathcal{O}(10^{-10})$ for the $\bar B_d^0 \to \phi
\gamma$, which are large enough for LHC-b and/or Super B-factories to detect
those channels in near future. Moreover, we also predict large CP asymmetries
in suitable parameter space. The observation of these modes could in turn help
us to constrain the $Z'$ mass within the model.
