A stretchable electronic device can retain its functionalities during high-level mechanical deformation, and stimulates the applications in the field of wearable and bio-implantable electronics. Efficient energy storage devices are an indispensable component in stretchable electronic systems. To integrate power supplies together with electronic devices that are mechanically flexible and stretchable, we demonstrate a new kind of stretchable all-solid-state supercapacitor, which consists of two slightly separated polyaniline/graphene electrodes in a wavy shape, with a phosphoric acid/polyvinyl alcohol gel as the solid-state electrolyte and separator. The as-fabricated wavy shaped supercapacitor was encapsulated in an elastomeric substrate which can be stretched to a large extent without mechanical degradation. The supercapacitor exhibited a maximum specific capacitance of 261 F g−1. Electrochemical cycling testing with the supercapacitor showed 89% capacitance retention over 1000 charge–discharge cycles at a current density of 1 mA cm−2. The bending and stretching tests showed that the supercapacitor maintained high mechanical strength and high capacitance simultaneously, even under a strain of 30%. This stretchable all-solid-state supercapacitor shows great potential as an energy storage device for stretchable electronic systems.