Graphene supports both transverse magnetic and electric modes of surface polaritons due to the intraband and interband transition properties of electrical conductivity. Here, we reveal that perfect excitation and attenuation-free propagation of surface polaritons on graphene can be achieved under the condition of optical admittance matching. With both vanished forward and backward far-field radiation, incident photons are fully coupled to surface polaritons. This requires an exact match between the admittance difference of sandwiching media and the conductivity of graphene, resulting in no decay of propagating surface polaritons. The dispersion relation has a completely different line shape for structures that support compared to those that do not support admittance matching. This work promotes complete comprehension of the excitation and propagation behaviors of graphene surface polaritons and may further inspire ideas for research on surface waves on two-dimensional materials.