• The NBT ceramic was prepared by solid state reaction. • Modified Debye theory has been adopted to describe the phenomenon of relaxation. • The temperature dependence of Dc-conductivity of NBT followed the Mott’s Variable Range Hopping (VRH) law. This work focuses on the structural, optical and electrical properties of sodium bismuth titanate Bi 1/2 Na 1/2 TiO 3 (NBT) lead-free ceramic for its possible application in capacitors, batteries and as an electrolyte in SOFC. NBT material was prepared by the solid-state method. X-ray diffraction analysis performed at room temperature revealed a rhombohedral structure with R3c space group. Rietveld refinement confirmed a good agreement between the calculated and the observed pattern. Scanning electron microscopy analysis revealed a polycrystalline nature of the material with a grain size of 29.17 µm. FT-IR analysis showed the presence of different bonds. The band gap energy was extracted through diffuse reflectance spectroscopy and was found to be 2.61eV. Detailed studies of dielectric and impedance properties carried out in the frequency range of 40–10 7 Hz at different temperatures (from 400K-700K) provided many interesting properties. The dielectric loss and dielectric constant with frequency increase. This behavior could be interpreted by the Maxwell–Wagner type of polarization in agreement with Koop's theory. To explain the complex impedance plane plots, an equivalent circuit template was employed, reflecting semiconducting behavior of NBT. The Ac-conductivity spectrum satisfied Jonscher’s power law below 460K and followed Jonscher’s double power law (DPL) above 480K. The correlated barrier hopping (CBH) and small polaron hopping (SPH) models could explain the conduction mechanism at the studied temperature range. The study of the Dc-electrical conductivity confirmed that NBT followed the variable range hopping (VRH) model. The present work could give further insights into this kind of material from a physical point of view and thus enhance its presence in the industrial field.