Polycrystalline graphene grown by chemical vapor deposition (CVD) is characterized by line defects and disruptions at the grain boundaries and nucleation sites. This adversely affects the stretchability and conductivity of graphene, which limits its applications in the field of flexible, stretchable, and transparent electrodes. We demonstrate a composite electrode comprised of a graphene/silver nanowires (AgNWs)/graphene sandwich structure on a polydimethylsiloxane substrate to overcome this limitation. The sandwich structure exhibits high transparency (>90%) and excellent conductivity improvement of the graphene layers. The use of AgNWs significantly suppresses the conductivity loss resulting from stretching. The mechanism of the suppression of the conductivity loss was investigated using scanning electron microscopy, atomic force microscopy, and lateral force microscopy. The results suggest that the high surface friction of the sandwich structure causes a sliding effect between the graphene layers would produce low crack or hole formation to maintain the conductivity. In addition to acting as conductive layers, the top and bottom graphene layers can also protect the AgNWs from oxidation, thereby enabling maintenance of the electrical performance of the electrodes over a prolonged period. We also confirmed the applicability of the sandwich structure electrode to the human body, such as on the wrist, finger, and elbow.