The electrical conductivity (EC) of minerals found on Earth and throughout the solar system is a fundamental transport property that is used to understand various dynamical phenomena in planetary interiors. High-pressure and high-temperature (P-T) EC measurements are also an important tool for observing phase transitions. Impedance measurements can accurately measure the EC of a nonmetallic sample. In previous measurements under static conditions using a laser-heated diamond-anvil cell (LHDAC), only direct current resistance is measured, but this method overestimates the bulk sample resistance. Moreover, the previous methodology could only be applied to nontransparent samples in an LHDAC using infrared lasers, limiting the range of measurable composition. To the best of our knowledge, no in situ high-P-T EC measurements of transparent materials have been reported using LHDAC techniques. We developed a novel impedance measurement technique under high-P-T conditions in an LHDAC that applies to transparent samples. As a validation, we measured the EC of Mg0.9Fe0.1SiO3 bridgmanite up to 51 GPa and 2000 K and found that the results are consistent with those of previous studies. We also measured the EC values of sodium chloride to compare with those of previous studies, as well as those of cubic boron nitride and zirconia cement to quantify how well they insulate under high P-T conditions. This is the first report of the impedance and EC measurements of transparent minerals in an LHDAC, which allows the measurement of Fe-poor/-free materials, including the major constituents of the interiors of gas giants and icy planets, under extreme conditions.