Reduced graphene oxide (RGO) doped polyvinyl alcohol/ Polyethylene glycol (PVA/PEG) films were prepared by solution casting technique and exposed to 100 kGy gamma radiation. The structural modifications in the samples before and after irradiation were studied using X-ray diffraction XRD, Fourier transform infrared spectroscopyFTIR anddifferential scanning calorimetry DSC. The free volume holes Vf determined from the o-Ps lifetime τ3measured by the positron annihilation spectroscopy (PALS) is found to decrease from (84.52 to 67.24Å3) and from (85.67 to 78.21 Å3) for nonirradiated and irradiated samples respectively with increasing the nanoscale RGO fillercontentto the polymer matrix. The resulting decrease of the free volume holes size due to this incorporation could be explained byboth the formation of hydrogen-bonding and crosslinking between RGO and PVA/PEG blend as confirmed byXRD and FTIR measurements. This also caused a decrease in the concentration of free volumes Fr for both nonirradiated and irradiated samples. The increased D.C. electrical conductivity with increasing RGOvolume fraction(0–0.265) suggests a conductivity chain formation through the nanoparticle aggregation. The deduced Ln σis found to be positively correlated with the probability of free annihilation of positrons I2, trapped at crystalline-amorphous interfaces. The D.C. conductivity results could be successfully fitted using the model suggested by Miyamoto and Shibayama. The critical free volumes for the charge carriers' transport has been deduced to be 80.34 and 82.16Å3 for nonirradiated and irradiated samples respectively.