Conductive hydrogels have garnered considerable attention as novel materials for biomedical devices and tissue engineering because they exhibit electroactivity and tissue-like softness. Various composites and manufacturing techniques have been developed in this regard. However, conductive hydrogels often exhibit poor mechanical properties (e.g., low toughness), which impedes their biomedical application. In this study, we fabricated double network (DN) hydrogels composed of sodium alginate (SA), polyacrylamide (PAAm), and graphene oxide (GO) to promote elasticity, toughness, and mechanical strength. Subsequently, we reduced the composite hydrogels to improve electrical conductivity by converting GO to more conductive reduced graphene oxide (rGO). The electrical, electrochemical, and mechanical properties of the produced hydrogels, r(GO/SA/PAAm), were characterized. Particularly, crosslinking density and reducing time were varied to obtain optimal conditions. The produced r(GO/SA/PAAm) demonstrated excellent electrical conductivity, mechanical strength, and toughness compared to homopolymers and unreduced DN hydrogels. We demonstrated that conductive DN hydrogels are suitable strain sensors. Electrically conductive and mechanically strong hydrogels will be beneficial in various biomedical applications, such as tissue engineering scaffolds and bioelectrodes.