Slow light devices have significant applications in memory, switching, and quantum optics. However, the design and fabrication of slow light devices with large tunable group delay are still challenging. Here, a graphene-based slow light device that can electrically modulate the group delay of terahertz (THz) waves is proposed and experimentally demonstrated. The unit cell of the device consists of a U-shaped metal resonator and an Ω-shaped metal resonator, with three graphene ribbons embedded between the two resonators. Under electrical stimuli, a relatively high amplitude modulation depth of 74% is achieved and the maximum transmission amplitude is as high as 0.7 at the transmission peak of 0.6 THz. Most importantly, the maximum group delay variation reaches 5 ps at 0.76 THz and the maximum group delay amplitude is as high as 8.8 ps. The experiment shows good agreement with simulation. This study paves a new way for developing novel switchable nanophotonic devices and slow light devices.