Nanostructure materials are of interest in last few decades due to their unique size-dependent physio-chemical properties. In this paper, zinc oxide (ZnO) and barium doped ZnO nanodisks (NDs) were synthesized using sonochemical method and characterized by various techniques such as X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscope (SEM), UV-vis absorption and dielectric measurements. The XRD and FTIR studies confirm the crystalline nature of ZnO NDs, and the average crystallite size was found to be ~25 nm for pure ZnO and ~22 nm for Ba doped ZnO NDs. SEM study confirmed the spherical shaped ZnO NDs with average sizes in the range of 20-30 nm. The maximum absorbance was obtained in the 200-500 nm regions with a prominent peak absorbance were observed by UV-vis spectra. The corresponding band gap for ZnO NDs and Ba doped ZnO NDs were calculated using Tauc's plot and was found to be 3.12 and 3.04, respectively. The conductivity and dielectric measurements as a function of frequency have been studied.