In this work facile sol-gel (pechni) method has been successfully established to synthesize Zn4B6O13 nanocrystals which have cubic crystals with lattice parameter: a =7.48 A. The structure and morphology of the obtained material were studied by X-ray diffraction (XRD), Infrared spectra (IR), scanning electron microscopy (SEM) and photoluminescence analysis. The experimental results show a band gap of 3.306 eV for the synthesized materials. Density functional theory (DFT) calculations by GGA-PBE method show, the crystals belong to the semiconductors with an indirect energy band gap of about 3.289 eV. The calculated band gap using the GGA-PBE method is comparable with the experimental results. The optical properties include the dielectric spectra; absorption, reflectivity and energy-loss spectra, and the origin of spectral peaks were analyzed based on the electronic structures.