Graphene is a one-atom thick layer of carbon atoms arranged in a hexagonal pattern, which makes it the strongest material in the world. The Tersoff potential is a suitable potential for simulating the mechanical behavior of the complex covalently bonded system of graphene. In this paper, we describe a new coarse-grained (CG) potential, TersoffCG, which is based on the function form of the Tersoff potential. The TersoffCG applies to a CG model of graphene that uses the same hexagonal pattern as the atomistic model. The parameters of the TersoffCG potential are determined using structural feature and potential-energy fitting between the CG model and the atomic model. The modeling process of graphene is highly simplified using the present CG model as it avoids the necessity to define bonds/angles/dihedrals connectivity. What is more, the present CG model provides a new perspective of coarse-graining scheme for crystal structures of nanomaterials. The structural changes and mechanical properties of multilayer graphene were calculated using the new potential. Furthermore, a CG model of a graphene aerogel was built in a specific form of assembly. The chemical bonding in the joints of graphene-aerogel forms automatically during the energy relaxation process. The compressive and recover test of the graphene aerogel was reproduced to study its high elasticity. Our computational examples show that the TersoffCG potential can be used for simulations of graphene and its assemblies, which have many applications in areas of environmental protection, aerospace engineering, and others.