A midinfrared band-tunable graphene-based plasmonic waveguide is analytically and numerically investigated to realize electromagnetically induced-transparency-like transmission and to slow rainbow trapping light. By applying different Fermi energy levels to the top and bottom graphene nanoribbons, a dynamic control of resonant wavelengths is thus obtained at the desired working regions. Plus, the structural size parameters play a significant role in modulating the resonant spectra and resonant depth. Combining the manipulation of the two sets of influential factors, the transparency window is therefore under control. Detailed investigations of the analytic mechanism of the device are made as well. Furthermore, the light signal that travels in the waveguide can be successfully slowed down to over 340 times the speed in a vacuum. If the nanoribbon width is gradiently distributed, the so-called rainbow trapping can be achieved. Hence, the device has potential applications in nanoimaging, sensing, integrated circuits, and light energy storage domains.