Generating appropriate tiny neutrino masses via inverse seesaw mechanism within the framework of a particular SU(3)xSU(4)xU(1) gauge model is the main outcome of this letter. It is achieved by simply adding three singlet exotic Majorana neutrinos to the usual ones included in the three lepton quadruplet representations. The theoretical device of treating gauge models with high symmetries is the general method by Cotaescu. It provides us with a unique free parameter (a) to be tuned in order to get a realistic mass spectrum for the gauge bosons and charged fermions in the model. The overall breaking scale can be set around 1-10 TeV so its phenomenology is quite testable at present facilities.