Theoretical studies of electrodes potential influence on the sensitivity and ratio of anode current and emission current (Igrid/Ie) will be beneficial for providing theoretical basis and experimental instruction in the research of ionization gauge with carbon nanotubes cathode. In this paper, based on the structure of IE514 extractor gauge, the model of carbon nanotube ionization gauge is built by ion optic simulation software SIMION 8.0. And the influence of electrode potential on the sensitivity and Igrid/Ie is discussed. Results show that with increasing ratio between anode voltage and gate voltage (Vgrid/Vgate), Igrid/Ie increases, while the sensitivity of the gauge decreases with the increase in anode voltage, which would further affect the extension of vacuum measurement lower limit. Moreover, the simulation results are in good agreement with the experimental data reported. Consequently, it is very important to improve the sensitivity, anode current and extension of measurement lower limit to set up an appropriate electrode voltage. In addition, the method adopted in this paper can be extended to the research and development of new-styles of extremely high vacuum ionization gauge of carbon nanotube cathode, which could provide an effective method to resolve the problem of extremely high vacuum measurement.