In order to improve the accuracy of resistivity logging through casing, numerical simulation research on instrument calibration and down-hole measurement was constructed. In the aspect of instrument calibration, the calibration device was modeled and the numerical simulation on instrument calibration was executed. In the aspect of down-hole measurement, the approximate method for current calculation was proposed, and the approximate current, the apparent formation resistivity and the second order potential difference of the thin layer and the thick layer were simulated numerically. The simulation results of instrument calibration help to select the parameter for the calibration device, provide the theoretical calibration curve and assist to calculate the coefficient of the electrode array. The simulation results of down-hole measurement show that the approximate method for current calculation has strong ability to distinguish layer boundaries, and the approximate degree of apparent formation resistivity for the thin layer with low resistivity drops obviously. The thick layer with high resistivity requires high instrument resolution because its second order potential difference is extremely small.