In this study, the effects of chemical functionalization on the elastic properties of graphene sheets are investigated by using molecular dynamics (MD) and molecular mechanics (MM) simulations. The influences of the degree of functionalization, which is defined as the ratio of the number of the total sp3-hybridized atoms to the number of the total carbon atoms of the graphene sheet, the chirality of graphene sheets, the molecular structure and molecular weight of functional groups on Young's modulus are studied. The dependence of shear modulus and wrinkling properties on the functional groups are also investigated. The simulation results indicate that Young's modulus depends strongly on the degree of functionalization and the molecular structure of the functional groups, while the effects of chirality of the graphene sheets and the molecular weight of the functional groups are negligible. The chemical functionalization also reduces the shear modulus and critical strain, beyond which the wrinkling instability occurs.