The importance of a good model for the $\gamma$-ray energy spectrum from the radiative thermal neutron capture on Gadolinium (Gd)
is specially increased in the present era of Gd-enhanced $\bar{\nu}_e$-search detectors. Its an essential prerequisite for MC studies to evaluate the neutron tagging efficiency, in order to enhance signal sensitivity in the Gd-loaded $\bar{\nu}_e$-search detectors. The $\gamma$-ray spectra produced from the thermal neutron capture on enriched gadolinium targets ($^{\rm 155}$Gd, $^{\rm 157}$Gd and Natural Gd) in the energy range 0.11 MeV to 8.0 MeV, were measured using the ANNRI Germanium Spectrometer at MLF, J-PARC. Based on the data acquired and a GEANT4 simulation of the ANNRI detector, we reported the energy spectrum of $^{\rm 157}$Gd(n, $\gamma$) and developed a $\gamma$-ray emission model of $^{\rm 157}$Gd(n, $\gamma$) in our previous publication. We now present the analysed data of $^{\rm 155}$Gd(n, $\gamma$) and $^{\rm nat}$Gd(n, $\gamma$) reactions, the energy spectra of $\gamma$-rays and an improved model for $^{\rm 155}$Gd(n, $\gamma$), $^{\rm 157}$Gd(n, $\gamma$) and $^{\rm nat}$Gd(n, $\gamma$) reactions. The consistency of the results from the devised model is checked among all the 14 germanium crystals, at the level of 15% spectral shape deviation at 0.2 MeV binning.