We propose a plasmonic waveguide comprising a single-layer graphene, a silica dielectric layer, and a silicon grating substrate to realize dual-channel slow surface plasmon polaritons. The dual-channel results from the introduction of two kinds of periodic structures with defects in the waveguide. According to the Bragg equation, we match the appropriate structure parameters to ensure the slow light dual-channel working around λ1=9369.1nm (32 THz) and λ2=7138.2nm (42 THz). The influence of the structure parameters on the slow light effect is discussed, and the largest value of the normalized delay bandwidth product (NDBP) is up to 7.38. Then, by shifting the gate voltage, obvious linear blueshift of the dual-channel is achieved. In this process, the slow light performance of the dual-channel exhibits good stability, and the average values of the NDBP are 4.5 and 4.4. Due to the flexible tunability, the waveguide may pave the way for the design of slow light devices.