In order to enhance cell power density and to study the interfacial electric property between beta "-alumina and an electrode, test cells of Na(1)/beta "-alumina/M, where M = TiN or TiB2 or Na-Sn or Na-Pb molten alloys as electrode materials, were set up and run within the temperature range of 400 degrees-800 degrees C. The performance of the test cells and the interfacial electric properties were investigated by measuring current-voltage characteristics and AC impedance. The maximum power density of 0.18 W cm(-2) for TiN and 0.24 W cm(-2) for TiB2 could be achieved with a large electrode-area of 30 cm(2) at 800 degrees C. A simplified model and equivalent circuit were given, based on the impedance data. The effect of microstructure of the porous electrode and roughness of the beta "-tube on the cell electric performance and impedance has been studied and discussed. The electron-transport through the porous electrode to the interface of the electrode and the beta "-tube surface is the control step for the electrode reaction, Na+ + e --> Na, rather than the mass-transport step, for a cell of Na(1)/beta "-alumina/porous thin film electrode. The AC impedance data demonstrated that wetting of the beta "-alumina electrolyte plays an important roll in reducing the cell resistance for the molten Na-Sn or Na-Pb electrode, and the molten alloy electrodes have a smaller cell-resistance, 0.3-0.35 Ohm cm(2), at 700 degrees C after 10-20 h. The comparison with sputtered thin, porous film electrodes, showed that the microstructure and thickness of electrode, and the interfacial resistance between electrode and the surface of the beta "-alumina is crucial to enhance cell power density.