The polycrystalline sample of bismuth based-complex multiferroic of a composition Bi0.5Pb0.5Fe0.5Ce0.5O3 was prepared by a high-temperature solid-state reaction technique (calcinations temperature = 900 °C, sintering temperature = 960 °C, time = 4 h). Preliminary structural analysis using XRD data exhibits the formation of a single-phase compound. Studies of surface morphology of the ceramic sample of the compound, recorded at room temperature using a scanning electron microscope, show uniform distribution of grains of different size with few voids. Detailed studies of dielectric properties (er, tan δ) supported the existence of multiferroic properties in the above complex system. The analysis of impedance parameters, recorded in a wide frequency (1 kHz–1 MHz) and temperature (room temperature to 450 °C) range of the material provide better understanding of (a) role of grains and grain boundaries in resistive and capacitative characteristics, (c) structure-properties relationship and (b) type of relaxation process occurred in the material. Study of temperature dependence of dc conductivity of the compound shows the existence of negative temperature coefficient of resistance in it. The nature of variation of ac conductivity with temperature of the material follows the Josher’s universal power law. Study of magneto-electric characteristics of the sample at room temperature has provided many useful and new data on magneto-electric coupling coefficient of different orders.