Stretchable and conductive hydrogels are rapidly emerging as new generation candidates for wearable devices. However, the poor electroactivity and bioadhesiveness of traditional conductive hydrogels has limited their applications. Herein, a mussel-inspired strategy is proposed to prepare a specific core-shell redox-active system, consisting of a polydopamine (PDA) modified zeolitic imidazolate framework 71 (ZIF-71) core, and a poly 3,4-ethylenedioxythiopene (PEDOT) shell. Owing to the abundant catechol groups, PEDOT can be assembled on the surface of ZIF-71 to create a redox-active system. The core-shell nanoparticles could act as a redox-active nanofiller to develop a conductive polyacrylamide (PAM) hydrogel with energy-storage properties. The core-shell PEDOT@PZIF-71 system provides a mussel-inspired environment in the hydrogel matrix and endows the hydrogel with stretchability and adhesiveness. The hydrogel can be applied as a functional electrode for both bioelectronics and supercapacitors. Moreover, this hydrogel exhibits favorable biocompatibility and can be implanted in vivo for biosignal measurement without causing inflammation. This redox-active core-shell PEDOT@PZIF-71 system provides a promising strategy for the design of hydrogel-based wearable electronic devices.