Impedance and electrical conduction studies of $Ba(Nd_{1/2}Nb_{1/2})O_3$ ceramic prepared using conventional high temperature solid-state reaction technique are presented. The crystal symmetry, space group and unit cell dimensions were estimated using Rietveld analysis. X-ray diffraction analysis indicated the formation of a single-phase cubic structure with space group $Pmar{3}m$. Energy dispersive X-ray analysis and scanning electron microscopy studies were carried to study the quality and purity of compound. The circuit model fittings were carried out using the impedance data to find the correlation between the response of real system and idealized model electrical circuit. Complex impedance analyses suggested the dielectric relaxation to be of non-Debye type and negative temperature coefficient of resistance character. The correlated barrier hopping model was employed to successfully explain the mechanism of charge transport in $Ba(Nd_{1/2}Nb_{1/2})O_3$. The ac conductivity data were used to evaluate the density of states at Fermi level, minimum hopping length and apparent activation energy.