A three-dimension model is set up to simulate the transport and electrochemical processes in mediator-enhanced solid-state supercapacitors. The roles of mediators are studied in wide ranges of mediator parameters, including concentration, conductivity, and diffusivity. The simulation results are validated using experimental data previously published. The simulation results show that with a concentration of mediators greater than 0.2 mol L-1 and diffusivity of mediators greater than 3 x 10(-12) m(2) s(-1) in electrodes, the charge/discharge behaviours are generally battery-like. The simulation results clearly reveal that if free ions are given off by mediators during the charging process, the specific capacity of the supercapacitors can be increased. The simulation results also indicate that if the diffusivity of mediators in the separator membrane is below 10(-12) m(2) s(-1), the self-discharge of the supercapacitor due to shuttling of the redox species between the electrodes is negligible. Thus, an operational mediator supercapacitor relies on a selective separator membrane and a high diffusivity of mediators in the composite electrodes.