AC conductivity of consolidated nanoparticles of NiO, having different average particle sizes (2.5 nm-17 nm) was measured in the temperature range 313 K to 413 K and over the frequency range 50 Hz to 3 MHz. The ac conductivity of the samples was found to be enhanced by six to eight orders of magnitude over that of NiO single crystals reported in the literature. This large enhancement in conductivity is attributed to the high density of Ni2+ vacancies in the nanoparticles. The variation of ac conductivity with frequency of the applied signal and temperature is discussed on the basis of the Correlated Barrier Hopping (CBH) Model. The observed spread in activation energy and slope of the log sigma (ac) Vs log omega plots is attributed to the distribution of the charge carrier hopping distance and localization energies in the nanoparticle samples. The effect of the interfacial region on the electrical conductivity of the samples is analyzed by taking into account the contributions due to grain boundaries and triple junctions. The observed variation of measured ac conductivity with average particle size is semi-quantitatively explained based on the reasoning that the role of the triple junctions is to reduce the conductivity.