A graphene-involved plasmonic lossy system that allows coupling between surface plasmon polaritons and waveguide modes is proposed. The physical mechanism behind the hybrid resonance modes is investigated carefully through finite element method (FEM) simulations and rigorous coupled wave theory (RCWA). We demonstrate that by introducing an incident angle to break the symmetry of the structure, the bound states in the continuum (BIC) evolve to an observable quasi-BIC with new resonance dips, and the generated signals possess a very high Q-factor. Such transformation is investigated carefully by calculating the band structure of the system and the corresponding Q-factors. The results showed that the calculated results from the band structure are consistent with the simulations. In addition, the hybrid plasmonic system allows for switching modulation due to the tunability of graphene, and the max modulation depth of nearly 100% is reached. The outstanding Q-factor and dynamic tunability of this easy-to-fabricate hybrid structure may be helpful in engineering various plasmonic devices, including tunable optical switches, absorbers, sensors, etc.