The invention relates to the field of energy saving, in particular to a double-regenerative burner and a burning system. The double-regenerative burner comprises a first regenerative chamber and a second regenerative chamber which are cylindrical, the problem that the temperature at the corners of a square regenerative chamber and the temperature at the middle portion of the regenerative chamber are inconsistent is greatly avoided, the heat contact area is increased, the heat conduction and heat storage performance of the whole regenerative chambers is enhanced, and the utilization rate of the heat is increased. The first regenerative chamber and the second regenerative chamber are both of a hexagonal honeycomb through hole structure, the contact area of a heat source is further increased, and the regenerative capacity and the heat conduction effect can be greatly enhanced. The burning system is provided with the double-regenerative burner and a turbo-charging assembly, the utilization rate of the heat is increased, and more energy is saved.