This paper reports a numerical study on carbon dioxide dissociation using a microhollow cathode discharge (MHCD) plasma reactor. These reactors can produce non-equilibrium plasmas and can be a promising technology for converting carbon dioxide into valuable chemicals and renewable fuels. However, these applications are currently in their early stages. In order to understand the effects of major design and operational parameters on the reactor performance a MHCD system was modeled and simulated. In this study, different types of dielectrics including mica, alumina, acrylic and quartz were used, and applied DC voltage was varied from 250 to 10,000 V. First the operating voltage regions of this reactor were determined based on the breakdown thresholds of the dielectric and gas phase. Then, the effects of applied voltage on the discharge volume and power requirement of operation were determined. Results showed that the reactor with mica as the dielectric material showed the largest operating voltage range, as well as the highest power requirement. In addition, the discharge volume increased with applied voltage and it was possible to discharge about 96% of the gas in the MHCD reactor with mica at 10 kV.