The electrical anisotropy of rock is characterized by conductivity tensor. The four-pole method and six-pole method are mostly used to measure rock conductivity in the laboratory，but it is difficult to fill the nine components of conductivity tensor in one experiment. And multiple experiments are easy to cause large measurement errors. For this reason，based on the existing document，this paper designs a conductivity tensor measuring instrument for square sample cores. This solution is also suitable for plunger cores. The completely water-saturated core is replaced by nitrogen. The temperature control system and the confining pressure control system control the temperature and pressure inside the core holder. The upper computer control electrode can be used to measure the core conductivity tensor at different water saturations. The instrument can also be used for rock electrical experiments of plunger cores. Through the measured conductivity data，the unknown coefficients of Archie’s formula can be determined. Through the analysis on theoretical and experimental data，the feasibility of the design scheme of the conductivity tensor measuring instrument is verified.