The invention discloses a combustion device, a control method thereof, and an oxygen-rich supply assembly. The combustion device comprises a main body and the oxygen-rich supply assembly. The main body comprises a combustor; the oxygen-rich supply assembly is used for providing oxygen-rich gas beneficial to combustion for the combustor and comprises a gas curtain forming structure; the gas curtainforming structure comprises a first channel structure arranged on the periphery of the combustor; an oxygen-rich gas channel for the oxygen-rich gas to circulate is formed in the first channel structure; an oxygen-rich gas outlet communicating with the oxygen-rich gas channel is formed in the first channel structure; and the oxygen-rich gas blown out from the oxygen-rich gas outlet forms a gas curtain on the periphery of the combustor. According to the combustion device provided by the invention, the first channel structure arranged on the periphery of the combustor is utilized for forming the oxygen-rich gas channel, so that the oxygen-rich gas blown out from the oxygen-rich gas outlet formed in the first channel structure can form the gas curtain on the periphery of the combustor, the heat efficiency is improved, the combustion temperature is improved, and the emission of harmful substances is reduced.