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High permittivity dielectrics ceramics are often used for commercial multilayer ceramic capacitors, actuators applications, and is highly promising materials for dynamic random access memory (DRAM) and microelectromechanical systems (MEMS) applications due to its very stable, high insulating characteristic against voltage. Many studies have been conducted to enhance the above mentioned properties and most of the improvements have been achieved by doping with a small quantity of additives with some ferroelectric perovskite lead and lead free compounds. Especially, Na 0.5 Bi 0.5 TiO 3 (NBT) is one of the promising materials for environmental friendly application in compare to lead based composition. Extensive studies have been made on NBT based relaxor ferroelectric ceramic with a simultaneous substitution of Ba 2+ and Zr 4+ at Asite and B-site having led to the establishment and acceptance of the "space charge" model on the basis of explaining their structure and dielectric properties. A Polycrystalline 0.92(Bi 0.5 Na 0.5 )Ba 0.08 Z 0.04 T 0.96 O 3 (0.08BNBZT) material has been prepared by conventional solid state reaction method. X-ray diffraction pattern reveals a tetragonal structure having lattice parameters. The diffuseness parameter =1.59 has been established the relaxor nature. The dielectric relaxation obeyed the Vogel-Fulcher relation. Impedance spectroscopy is a convenient tool to evaluate the contribution of electrical components such as grain (g) (bulk), grain-boundary (g b ) or polarization phenomena, which influences the device properties of a material. Conductivity studies in the materials obey the Jonscher's power Law in frequency (45Hz -5MHz), temperature (35 0 C-600 0 C) range.