We report the impedance spectroscopy (IS) behavior of the ferroelectric- ferromagnetic (50% BaTi O3-50% La0.7Sr0.3MnO3) nano-composite prepared by sol-gel method. Frequency and temperature dependence of the complex impedance and conductivity has been measured over the temperature range 310 K-430 K. A distribution of relaxation times and decentralization of the semicircle has been observed from the Cole–Cole plots of real and imaginary parts of the complex impedance. Non-Debye type relaxation has been observed in the investigated composite system. An equivalent circuit has been constructed to describe the IS. Interestingly, a typical universal dielectric response in the frequency-dependent conductivity at different temperature has been found. The frequency dependent ac conductivity at different temperature indicates that the conduction process is thermally activated. The activation energy has been obtained from the Arrhenius fitting. The obtained dc conductivity showed that the system undergoes a positive temperature coefficient resistance (PTCR) to negative temperature coefficient resistance (NTCR) near 350 K. The results would help to understand deeply the relaxation process in these types of materials.