Thermal conductivity of free-standing reduced graphene oxide films subjected to a high-temperature treatment of up to 1000 °C is investigated. It is found that the high-temperature annealing dramatically increases the in-plane thermal conductivity, K, of the films from ≈3 to ≈61 W m^-1 K^-1 at room temperature. The cross-plane thermal conductivity, K, reveals an interesting opposite trend of decreasing to a very small value of ≈0.09 W m^-1 K^-1 in the reduced graphene oxide films annealed at 1000 °C. The obtained films demonstrate an exceptionally strong anisotropy of the thermal conductivity, K/K ≈ 675, which is substantially larger even than in the high-quality graphite. The electrical resistivity of the annealed films reduces to 1-19 Ω □^-1. The observed modifications of the in-plane and cross-plane thermal conductivity components resulting in an unusual K/K anisotropy are explained theoretically. The theoretical analysis suggests that K can reach as high as ≈500 W m^-1 K^-1 with the increase in the sp² domain size and further reduction of the oxygen content. The strongly anisotropic heat conduction properties of these films can be useful for applications in thermal management.