Surface plasmon polaritons enable light concentration within subwavelength regions, opening thereby new avenues for miniaturizing the device and strengthening light-matter interactions. Here we realize efficient electro-optic modulation in low-loss plasmonic waveguides with the aid of graphene, and the devices are fully integrated in the silicon-on-insulator platform. By advantageously exploiting low-loss plasmonic slot-waveguide modes, which weakly leak into a substrate while featuring strong fields within the two-layer-graphene covered slots in metals, we successfully achieve a tunability of 0.13 dB μm-1 for our fabricated graphene-plasmonic waveguide devices with extremely low insertion loss, which outperforms previously reported graphene-plasmonic devices. Our results highlight the potential of graphene plasmonic leaky-mode hybrid waveguides to realize active ultra-compact devices for optoelectronic applications.