We created a new graphite-Cu(II) electrode and found that the electrode could catalyze FADH$_2$ oxidation and FAD reduction coupled to electricity production and consumption, respectively. In a fuel cell with graphite-Cu(II) anode and graphite-Fe(III) cathode, the electricity was produced by coupling to the spontaneous oxidation of FADH$_2$ Fumarate and xylose were not produced from the enzymatic oxidation of succinate and xylitol without FAD, respectively, but produced with FAD. The production of fumarate and xylose in the reactor with FAD electrochemically regenerated was maximally 2- 5 times higher than that in the reactor with FAD. By using this new electrode with catalytic function, a bioelectrocatalysts can be engineered; namely, oxidoreductase (e.g., lactate dehydrogenase) and FAD can function for biotransformation without an electron mediator and second oxidoreductase for cofactors recycling.