The invention discloses an oxygen-enriched burning system and a combustion method thereof. A burner body is arranged. A fire ejecting hole is arranged in the middle of the burner body. A fuel distributor is arranged at one end of the small hole of the fire ejecting hole. Primary and secondary oxygen nozzles, an igniter, a flame monitor and a fire viewing hole passing through the burner body in the same direction of the fire ejecting hole are arranged on the periphery of the fire ejecting hole on the burner body. A flange plate connected with a fuel inlet pipe is arranged on the outer port of the fuel distributor. Both outer ports of the primary and secondary oxygen nozzles are provided with the flange plate connected with the fuel inlet pipe. The oxygen nozzles are connected with an oxygen supply system. A fuel cyclone separator is connected with a fuel supply system. A control cabinet is additionally arranged so that the full system of the whole burner is detected and controlled. The burner disclosed by the invention is applicable to combusting gases and powdered fuels. The burner has the advantages of complete structure, high combustion efficiency, little smoke discharge, environment protection, energy saving and high operation automation degree.