A three-dimensional computational model is presented in this paper that illustrates the detailed electrical characteristics, and the current–voltage (i–v) relationship throughout the preheating process of premixed methane-oxygen oxyfuel cutting flame subject to electric bias voltages. As such, the equations describing combustion, electrochemical transport for charged species, and potential are solved through a commercially available finite volume computational fluid dynamics (CFD) code. The reactions of the methane-oxygen (CH4–O2) flame were combined with a reduced mechanism, and additional ionization reactions that generate three chemi-ions, H3O+, HCO+, and e−, to describe the chemistry of ions in flames. The electrical characteristics such as ion migrations and ion distributions are investigated for a range of electric potential, V ∈ [−5 V, +5 V]. Since the physical flame is comprised of twelve Bunsen-like conical flames, inclusion of the third dimension imparts the resolution of fluid mechanics and the interaction among the individual cones. It was concluded that charged “sheaths” are formed at both torch and workpiece surfaces, subsequently forming three distinct regimes in the i–v relationship. The i–v characteristics obtained from this study have been compared to the previous experimental and two-dimensional computational model for premixed flame. In this way, the overall model generates a better understanding of the physical behavior of the oxyfuel-cutting flames, along with more validated i–v characteristics. Such understanding might provide critical information toward achieving an autonomous oxyfuel-cutting process.