In this work, the dielectric behaviour and capacitance–voltage (C–V) curves under an applied DC bias field of 1wt% Nb-doped CaCu3Ti4O12 ceramics have been studied. The dielectric properties reveal the existence of grain boundaries of different electrical nature. A new model is proposed to simultaneously explain the presence of insulating and conducting grain boundaries. At low frequency, the capacity curve of the material exhibits a double metal oxide semiconductor (MOS) capacitor-like behaviour and as the frequency is increased, the curve suffers an inversion showing a ferroelectric-like response. This behaviour does not correspond to ferroelectric domain movement phenomena but seems associated to charge accumulation on grain boundary regions.