This paper reports a numerical study of coupled double diffusive convection and radiation in a differentially heated square enclosure filled with non-grey air–CO2 (or air–H2O) mixtures. The numerical procedure is based on a hybrid scheme with the multiple relaxation time lattice Boltzmann method and the finite difference method. The fluid velocity is determined by the D2Q9 multiple relaxation time model, and the energy equation is discretized by the finite difference method to compute the temperature field, while the radiative part of the energy equation is calculated by the discrete ordinates method combined with the spectral line-based weighted sum of grey gases model. Depending on the boundary conditions, aiding and opposing flows occur as the result of temperature and concentration gradients. The effects of various parameters, such as the molar fraction on the flow structure, thermal and concentration fields, are investigated for aiding and opposing cases. The numerical results show that, in the presence of non-grey radiation, the heat transfer is decreased and the mass transfer is slightly modified. The gas radiation modifies the structure of the velocity and thermal fields by generating inclined stratifications and promoting instabilities in opposing flows.