Abstract: Radiative (B) over bar (0)((B) over bar (0)(s)) -> J/psi gamma decays provide an interesting case to test our understanding of ( non) perturbative QCD and eventually to probe physics beyond the standard model. Recently, the LHCb Collaboration reported an upper bound, updating the results of the BABAR Collaboration. Previous theoretical predictions based on QCD factorization or perturbative QCD have shown large variations due to different treatment of nonfactorizable contributions and meson-photon transitions. In this paper, we report on a novel approach to estimate the decay rates, which is based on a recently proposed model for B decays and the vector meson dominance hypothesis, widely tested in the relevant energy regions. The predicted branching ratios are Br[(B) over bar (0) -> J/psi gamma] = (3.50 +/- 0.34(-0.63)(+1.12)) x 10(-8) and Br[(B) over bar (0)(s) -> J/psi gamma] = (7.20 +/- 0.68(-1.30)(+2.31)) x 10(-7). The first uncertainty is systematic and the second is statistical, originating from the experimental (B) over bar (0)(s) -> J/psi gamma branching ratio.