In this work, an improved quark model approach to the $\omega$ meson photo-production with an effective Lagrangian is presented. The {\it t}-channel {\it natural}-parity exchange is taken into account through the Pomeron exchange, while the {\it unnatural}-parity exchange is described by the $\pi^0$ exchange. With a very limited number of parameters, the available experimental data in the low energy regime can be consistently accounted for. We find that the beam polarization observables show sensitivities to some {\it s}-channel individual resonances in the $SU(6)\otimes O(3)$ quark model symmetry limit. Especially, the two resonances $P_{13}(1720)$ and $F_{15}(1680)$, which belong to the representation $[{\bf 56, ^2 8}, 2, 2, J]$, have dominant contributions over other excited states. Concerning the essential motivation of searching for "missing resonances" in meson photo-production, this approach provides a feasible framework, on which systematic investigations can be done.