In this paper, an atomistic based finite element model is developed to investigate the influence of topological defects on mechanical properties of graphene. In general, plane stiffness matrix of the hexagonal network structure of graphene is found. The effective elastic modulus of a carbon ring is determined from the equivalence of molecular potential energy related to stretch and angular deformation. A hexagonal carbon ring as a unit cell of the graphene sheet is modeled by four-node elements. Applying three-node triangular elements, Stone-Wales (SW) defect which is an important topological defect is also modeled. In this method, both pristine structure of graphene and graphene with SW defect are considered and to get more real structure, an atomistic model of a small part of graphite sheet around the defect site, is modeled in Gaussian software and new arrangement around SW defect are obtained by minimizing its energy. Young’ s modulus, shear modulus and Poisson’ s ratio of the pristine single-layered graphene sheet (SLGS) and the effect of topological defects on the elastic properties of SLGS were examined. The numerical results from this new model showed good agreement with data available in literature.