This work analyzes the spontaneous emission of a single emitter placed near the graphene waveguide formed by two parallel graphene monolayers, with an insulator spacer layer. In this case, the eigenmodes supported by the structure, such as surface plasmon and wave guided modes, provide decay channels for the electric dipole placed close to the waveguide. We calculated the contribution to the decay rate of symmetric and antisymmetric eigenmodes as a function of frequency and the orientation of the emitter. Our results show that the modification of the spontaneous emission due to excitation of guided modes is much lower than the corresponding decays through the excitation of symmetric and antisymmetric surface plasmons, for which, the spontan...