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Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified <i>Nu</i> scaling law in small <i>Pr</i> range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large <i>Pr</i>. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the <i>Nu</i> of radiative RB convection.