It is studied the thermal conductivity of graphene periodically embedded with four- and eight- membered rings (GFERs) by using non-equilibrium molecular dynamics simulations. This kind of structure has been experimentally synthesized recently. The dependence of thermal conductivity on the length (L) and temperature(T) is investigated. It is found that the thermal conductivity of GFERs is significantly lower than that of pristine graphene. On the other hand, the length dependence of thermal conductivity follows ~ logL behavior. In addition, the temperature dependence of thermal conductivity of GFERs follows ~T−α behavior. It is also found that there exists a large thermal rectification (TR) in graphene-GFERs heterostructures, the heat flux from the pristine graphene to the GFERs direction is larger than that in the opposite direction. The dependence of the TR ratio on system parameters is investigated.