An electrical conductivity measurement system under high-pressure conditions with a multi-anvil high-pressure apparatus by an ac complex impedance method was set up. With this system, we have successfully measured the electrical conductivity of synthetic quartz under pressure up to approximately 1.0 GPa in the temperature range 661-987K. The values of electrical conductivity decrease with the increasing pressure and increase with the increasing temperature. The activation enthalpies for the α-quartz crystals are 1.10-1.28eV. The electrical conductivity of α-quartz is ionic, with Na ions moving in channels parallel to the c-axis being the predominant current carrier.