A four-temperature kinetic-theory approach for modeling vibrationally non-equilibrium carbon dioxide flows is developed. The model takes into account all kinds of vibrational-translational energy transitions and inter-mode vibrational energy exchange between symmetric, bending, and asymmetric CO2 modes. The key feature of the model is using the averaged state-resolved relaxation rates instead of conventional Landau-Teller expressions. Spatially homogeneous CO2 vibrational relaxation is studied using the state-to-state, new four-temperature and commonly used three-temperature models. Excellent agreement between four-temperature and state-to-state solutions is found, whereas using the three-temperature model with the Landau-Teller production rates leads to significant loss of accuracy. Numerical efficiency of various approaches is discussed as well as the ways for its improvement.