Graphene plasmons, collective oscillation modes of electrons in graphene, have recently attracted intense attention in both the fundamental researches and the applications because of their strong field confinement, low loss and excellent tunability. The dispersion of graphene plasmons can be significantly modified in the system of graphene on metal substrate, in which the screening of the long-range part of the electron-electron interactions by nearby metal can lead to many novel quantum effects, such as acoustic plasmons, quantum nonlocal effects and renormalization of band structure. Scattering-type scanning near-field optical microscopy (s-SNOM) which consists of a laser coupled to the tip of an atomic force microscopy (AFM), is an effective technique to directly probe plasmons in two-dimensional materials including graphene, and the graphene plasmons can be observed visually by real-space imaging. But so far the detailed s-SNOM studies of graphene/metal system have not been reported. One potential challenge is that the near-field response of highly conductive metal substrate may partially or entirely obscure that of graphene, making it difficult to further explore graphene by using s-SNOM. Here in this paper, we report the direct observation of near-field optical response of graphene in a graphene/metal system excited by a mid-infrared quantum cascade laser. From a close examination of the data of graphene/Cu compared with that of h-BN/Cu, we are able to identify experimental features due to the near-field response of graphene. Surprisingly, two completely different behaviors are observed in the s-SNOM data for different graphene samples on Cu substrates with similar surface step geometries. These results suggest that the near-field response of graphene/metal system is not completely dominated by the metal substrate, and that two completely different near-field response behaviors of graphene may be attributed to their intrinsic properties affected by metal substrates themselves rather than surface step geometries of metal substrate. In addition, following this approach it is possible to distinguish the near-field optical responses of graphene from that of graphene/metal system. Our work reveals the clear signatures of the near-field optical response of graphene on metal substrate, which provides the foundation for probing plasmons in these systems by using the s-SNOM and understanding many novel quantum phenomena therein.