Transparent, stretchable films of carbon nanotubes (CNTs) have attracted significant attention for applications in flexible electronics, while the lack of structural strength in CNT networks leads to deformation and failure under high mechanical load. In this work, enhancement of the strength and load transfer capabilities of CNT networks by chemical vapor deposition of graphene in the nanotube voids is proposed. The graphene hybridization significantly strengthens the CNT networks, especially at nanotube joints, and enhances their resistance to buckling and bundling under large cyclic strain up to 20%. The hybridized films show linear and reproducible responses to tensile strains, which have been applied in strain sensors to detect human motions with fast response, high sensitivity, and durability.