This paper presents a hybrid lattice Boltzmann solver for turbulent buoyancy-driven flow coupled with surface thermal radiation. The two-relaxation time scheme for the Boltzmann equation combined with the implicit finite difference scheme for the energy equation is implemented to compute the heat transfer and fluid flow characteristics. The accuracy and robustness of the hybrid approach proposed in this study are assessed in terms of the numerical and experimental data of other researchers. Upon performing the simulation, the Rayleigh number is ranged from 108 to 1010 whereas the surface emissivity is changed from zero to unity. During computations, it is found that the overall temperature of the cavity is increased as a result of enhancing the surface radiation. Convective plumes are formed both at the isothermal and the thermally-insulated walls with the $Ra≥10^9$ and $ε≥0.6.$ In the conditions under study, the overall heat transfer rate is raised by around 5% when taking into account the surface thermal radiation.