Stretchable conductive elastomers have aroused great interest in recent years as candidates for smart rubber materials. A single conductive filler embedded in an elastomer matrix has been demonstrated to provide electrically conductive pathways, but the filler network can be improved by adding a second conductive filler. Herein, reinforced conductive epoxidized natural rubber (ENR) composites were designed to have hybrid nanostructures of multiwalled carbon nanotubes (MWCNT) with few-layer graphene (FLG) nanofillers. With both MWCNT and FLG, the ENR nanocomposites exhibited improved mechanical performance, filler dispersion, and electrical properties. The tensile strength of ENR filled with MWCNT and FLG was remarkably improved, and the Halpin-Tsai model revealed effective reinforcement by the MWCNT/FLG hybrid filler. Meanwhile, the electrical percolation threshold was decreased by 70% from 1.19 vol% for single nanofiller to 0.36 vol% for hybrid nanofiller. The main reasons for remarkable boosting of desirable characteristics of the hybrid nanocomposites are the uniform filler dispersion and the bridging between MWCNT and FLG through π-π interactions and filler-rubber interactions. Thus, ENR reinforced with hybrid nanostructures is a highly promising advanced conductive elastomeric material for smart rubber applications.