In order to reduce power consumption and realize ultrafast response time and dynamic tunability, a plasmonic waveguide system based on four disk resonators is designed. A plasmon induced transparency effect is theoretically analyzed by using two different methods: one is the direct destructive interference between bright mode resonator and dark mode resonator, and the other is the indirect coupling through a plasmonic waveguide. Owing to the giant effective nonlinear Kerr coefficient of the graphene-Ag composite material structure and the enhancement characteristics of slow light response to optical Kerr effect, the pump intensity of PIT system for changing the phase shift of transmission spectrum is greatly reduced. An ultrafast response time of 1 ps is achieved, and 0.4π, 0.8π, 1.2π, 1.6π and 2π-phase shift of the transmission spectrum in the plasmon induced transparency system are achieved with the intensity of the pump light as low as 2.34, 4.68, 7.02, 9.36, 11.7 MW/cm^–2, respectively. In this work, a plasmonic waveguide coupled directly by two small disk resonators is employed, because two small disk resonators play a role of the slit between the waveguide and the resonators, and also act as two separate resonators side-coupled with a plasmonic waveguide, which leads to the more efficient coupling of electromagnetic energy in the waveguide into the big disk resonators to form resonance and easier storage of light in the resonator. The triple-band plasmon induced transparency (PIT) effect and slow light properties of the model are analyzed by the expression of the deduced theoretical transmittance based on the coupled mode theory, indicating that they are very consistent with the finite-difference time-domain simulations. The results show that the transmission peak of the system is over 80% and the maximum group index is as high as 368. Furthermore, the disk resonators are easy to fabricate and the size of the entire PIT structure is < 0.5 μm², which is beneficial to the design of optoelectronic device on-chip integration. The research results have important application prospects in highly integrating optical circuits and networks, and also provide the ideas for the design and fabrication of multi-channel optical filter and light storage devices with low power consumption, ultrafast nonlinear response, ultracompact and dynamical tunability.