Polycrystalline (Bi0.5Na0.5)1-xBaxTiO3 [here after BNBT], x = 0, 0.02, 0.04, 0.06, 0.08, and 0.1 ceramics have been synthesized by conventional solid state reaction process and were characterized by X-ray diffraction technique, which indicates that on substitution of Ba 2+ in Bi0.5Na0.5TiO3 (BNT) ceramic there is splitting of the (2 0 0) peak for x ≥ 0.06. This splitting in the peak position reveals that the composition BNBT-0.06 is well in Morphotropic Phase Boundary (MPB) region where rhombohedral and tetragonal phase co-exist. Scanning electron micrograph shows decrease in grain size from 0.66 to 0.53 μm with increasing concentration of Ba 2+ ; and the dielectric constant of Ba 2+ doped BNT ceramics increased with decreasing grain sizes and a maximum value was attained at size of 0.54 ~ 0.56 μm. Doped BNT ceramic also exhibit diffuse phase transition and are characterised by a strong temperature and frequency dispersion of the permittivity which would be connected with the cation disorder in A-site of perovskite unit cell. Complex impedance spectroscopy is used to analyze the electrical behaviour of BNBT, which indicates the presence of grain effect and the composition exhibits Negative Temperature coefficient of resistance (NTCR) behaviour. The compounds exhibit Arrhenius type of electrical conductivity and the presence of non-Debye type of relaxation has been confirmed from impedance analysis.