The magnetic impurity effects and the existence of bound states (i.e. Yu-Shiba-Rusinov states) in superconductors have been a topic of great interest. Recently, the existence of Yu-Shiba-Rusinov states in graphene-based superconducting materials has been successfully observed in the laboratory. In this work, an effective Hamiltonian in real space is established to describe the superconducting state of graphene materials by considering a single magnetic impurity. Thus the Bogoliubov-de Gennes (BdG) equation is constructed and the self-consistency calculations of the superconducting order parameter are conducted. On this basis, the effects of magnetic impurities on graphene-like superconductors are investigated theoretically. The numerical results show that the Yu-Shiba-Rusinov state can only appear in the symmetry of the superconducting pair of the traditional s-wave coupling. The position and strength of the bound state are related to the magnetic moment of the impurity, showing a notable electron-hole asymmetry. There are no bound states in the energy gap for other pairing symmetries. This theoretical calculation not only provides a reasonable explanation for experimental phenomena, but also demonstrates that the heterojunction system composed of graphene and traditional superconductors has an s-wave superconducting pairing induced by the proximity effect in the graphene layer.