Thermal properties are essentially decided by atomic geometry and thus stress is the most direct way for manipulating. In this paper, we investigate stress modulation of thermal conductivity of graphene by molecular dynamics simulations and discuss the underlying microscopic mechanism. It is found that thermal conductivity of flexural-free graphene increases with compression and decreases with strain, while thermal conductivity of flexural-included graphene decreases with both compression and strain. Such difference in thermal behavior originates from the changes in the anharmonicity of the interatomic potential, where the wrinkle scattering is responsible for the thermal conductivity diminishment in flexural-included graphene under strain. By comparing the results obtained from the Tersoff and AIREBO potentials, it is revealed that the degree of the symmetry of interatomic potential determines the thermal conductivity variation of graphene. Our results indicate that the symmetry of interatomic potential should be taken into careful consideration in constructing the lattice model of graphene. Thermal properties are one decided by at atomic geometry and thus stress is the most direct way for manipulating. In this paper, we investigate stress modulation of thermal conductivity of graphene by molecular dynamics simulations and discuss the underlying microscopic mechanism. It is found that thermal conductivity of flexural-free graphene increases with compression and decreases with strain, while thermal conductivity of flexural-included graphene decreases with both compression and strain. for comparing the results obtained from the Tersoff and AIREBO potentials, it is revealed that the degree of the symmetry of interatomic potential determines the thermal conductivity variation of graphene. Our results indicate that the symmetry of in teratomic potential should be taken into careful consideration in constructing the lattice model of graphene.