As a quasiparticle formed by light and conduction electrons in graphene, surface plasmon polaritons (SPPs) due to their tight confinement to light and long propagation distances are promising for developing quantum interconnect devices. However, the significant damping of SPPs in the material generally causes the loss of quantum information, which greatly hinders its application. We here propose a mechanism to overcome the destructive effect of the damping SPP on the dynamics of a quantum emitter (QE). Via investigating the near-field coupling between QE and the SPP in a graphene nanodisk, we find that, with the complete dissipation of the QE efficiently avoided, quantum information of QE can be stabilized even toits steady state. This is caused by that, with decreasing the QE-graphene distance, the QE becomes so hybridized with the SPP that one bound state is formed between them. Our result supplies a useful way to avoid the impact of SPPs damping, which lays a foundation for developing quantum polaritonic devices.