  We investigate the pure annihilation type radiative $B$ meson decays $B^0 \to
\phi \gamma$ and $B_s \to \rho^0(\omega)\gamma$ in the soft-collinear effective
theory. We consider three types of contributions to the decay amplitudes,
including the direct annihilation topology, the contribution from the
electro-magnetic penguin operator and the contribution of the neutral vector
meson mixings. The numerical analysis shows that the decay amplitudes are
dominated by the $\omega-\phi$ mixing effect in the $B^0 \to \phi\gamma$ and
$B_s \to \omega\gamma$ modes. The corresponding decay branching ratios are
enhanced about three orders of magnitudes relative to the pure annihilation
type contribution in these two decay channels. The decay rate of $B_s \to
\rho^0\gamma$ is much smaller than that of $B_s \to \omega\gamma$ because of
the smaller $\rho^0-\phi$ mixing. The predicted branching ratios
$B(B^{0}\rightarrow\phi\gamma)=(3.99^{+1.67}_{-1.46}
)\times10^{-9},\,B(B_s\rightarrow\omega\gamma)=(2.01^{+0.81}_{-0.71}
)\times10^{-7}$ are to be tested by the Belle-II and LHC-b experiments.
