High-quality and large-size single crystals of lead-free Na_0.5Bi_0.5TiO₃ were grown using the Czochralski technique. The crystals had a pure perovskite structure with rhombohedral symmetry (R3c) and were translucent in the visible and near-infrared spectral ranges recorded in the interval 350-1050 nm. The energy gaps determined from the X-ray photoelectron spectroscopy (XPS) and optical measurements were approximately 2.92 eV. The density of the electronic states and energy band structures were investigated using an ab initio method. The energy gap calculated for NBT (R3c) was 2.8 eV, which is comparable to those determined from XPS and optical measurements. As calculations have shown, when the potentials intended for perovskites are applied to Na and Ti atoms, the energy gap value increases by 68% from 1.9 eV to 2.8 eV. The frequency/temperature dependent electrical properties were also measured and analyzed through complex impedance spectroscopy. An overlapping reversible insulator–metal transition (resistive switching) on nanoscales, caused by the electric field, was detected. This was the first time that most of these investigations were performed for this material. The activation energy values determined from the conductivity data, the imaginary part of the electric impedance and the modulus indicate that the relaxation process in the high-temperature range is attributable to both single and double ionized oxygen vacancies, in combination with the hopping of electrons between Ti⁴⁺ and Ti³⁺. P-type electrical conductivity was also found. These discoveries create new possibilities of reducing the electrical conductivity of NBT and improving the process of effectively poling this material.