Constructing an integrated system with high-efficiency and stable energy conversion and storage (ECS) is of great significance but remains challenges. Herein, we report a biodevice consisting of a bioanode of tetrathiafulvalene/glucose oxidase (TTF/GOx) immobilized on asphalt-derived porous carbon (APC) for catalyzing glucose oxidation and a biocathode of 2,2’-azinobis(3-ethylbenzothiazoline-6-sulfonate)/bilirubin oxidase (ABTS/BOD) immobilized on APC for catalyzing oxygen reduction, to achieve ECS with high-efficiency and excellent stability. The redox mediators, TTF and ABTS, used at the bioanode and biocathode, respectively, simultaneously mediate electron transfer to release electric current on discharging and serve as pseudocapacitors to achieve charge storage at open-circuit conditions, enabling high power density and self-charge capability. The biodevice of the above configuration delivers a peak power output of 5.01 mW cm−2 in the pulse discharge mode with cell voltage remaining 93.7 % of its initial value after 100 pulse discharge/self-charge cycles. This work provides a highly efficient solution to address the low power density and poor stability of the conventional enzymatic biofuel cells, showing great implications for small, implantable and wearable electronics.