Carrier transport through electrically active grain boundaries has been studied under biased condition using Solartron 1260 impedance/gain phase analyzer with an applied AC potential of 250 mV in the frequency range 1 Hz–1 MHz for nanocrystalline TiO2 and CeO2 as the model systems. Prior to the measurement both the materials were converted into cylindrical pellets with (8 mm diameter and 1 mm thick) by applying uni-axial pressure of 4 ton using a hydraulic press, then sintered at 300, 450 and 600 °C for 30 min for TiO2 sample and for the case of CeO2 it was done at 300, 600 and 900 °C for 30 min. Further, they were characterized using powder X-ray diffractometer (XRD) and transmission electron microscopy (TEM) to know the crystal structure, average crystallite size and morphology. The impedance measurements were performed at room temperature under applied DC bias voltages from 0 to 3 V in the periodic increment of 0.2 V. The observed applied bias voltage effect on dielectric constant of both the systems was analyzed with ‘grain boundary double Schottky potential barrier height model’ for different grain sizes. The percentage of voltage tunable dielectric constant (T%) as a function of frequency was estimated for all the grain sizes and it was found to be increase with reduction of grain size. Our experimental findings reveal the possibilities of utilizing these nanocrystals as a potential active material for phased array antenna since both the samples exhibits T% = 85% at 100 Hz frequency.