A novel redox flow battery based on soluble organic redox active material is attracting increasing research attention, which employs a family of molecules known as quinones. A three dimensional numerical model of the novel flow battery with a flow through electrode has been developed. The electric current density and the ion current density along the electrode thickness under different specific areas and different electrode conductivities are analyzed, accounting for the electrode thickness effect on the cell performance. It can be concluded that six layers of carbon paper is the most appropriate electrode thickness. More than six layers of carbon paper provides more surface area at the expense of higher ohmic resistance, which is not appropriate. Less carbon paper cannot provide enough specific active area. The flow fields in the x direction and z direction are analyzed to account for the electric current density distribution. The high current density at the junction of the land and channel for the flow through electrode cell is related to the flow field in z direction. The simulation results are well-fitted for the experiment data. In addition, we improve the previously existing electrolyte conductivity calculation model and demonstrate that accurate electrolyte conductivity values are required for accurate modeling of the experiment. The model is validated using data obtained from combining a quinone/hydroquinone couple with a Br2/Br− redox couple flow battery system.