Since flow-electrodes do not have a maximum allowable charge capacity, a high salt removal rate in flow-electrode capacitive deionization (FCDI) can be achieved theoretically by simply increasing the applied voltage. However, present attempts to run FCDI at high voltages are unsatisfactory because of the instability of the module occurring in the overlimiting current regimes. To implement FCDI in the overlimiting current regimes (namely, OLC-FCDI), in this work, we analyzed the voltage-current (V-I) characteristics of several FCDI units. We confirmed that a continuous, rapid, and stable desalination performance of OLC-FCDI can be attained when the employed FCDI unit possesses a linear V-I characteristic (only one ohmic regime), which is distinct from the three V-I regimes in electrodialysis (ohmic, limiting current, and water splitting regimes) and the two in membrane capacitive deionization (ohmic and water splitting regimes). Notably, the linearV-I characteristic of FCDI requires continuous charge percolation near the boundaries of ion-exchange membranes. Effective methods include increasing the carbon content in the flow-electrodes and introducing electrical (carbon cloth) or ionic (ion-exchange resins) conductive intermediates in the solution compartment, which result in corresponding upgraded FCDI units exhibiting extremely high salt removal rates (>100 mg m-2 s-1), good cycling stability, and rapid seawater desalination performance under typical OLC-FCDI operation condition (27-40 g L-1 NaCl, 500 mA). This study can guide future research of FCDI in terms of flow-electrode preparation and device configuration optimization.