In this study, we developed the design process and optimization of structural parameters of a new low-NOx burner based on low-NOx combustion technology and the flame stabilization principle. Firstly, on the basis of the two-stage swirl burner, we applied the fuel-graded combustion technology and introduced the central nozzle structure to explore the influence law of graded combustion on NOx emissions. Secondly, on the previously optimized structure, the matching law between the first- and second-stage cyclone blades is analyzed to obtain the optimum structural design solution for heat exchange efficiency and flame front length. Finally, a new conical blunt structure is introduced in conjunction with the flame stabilization principle, and we discuss the effects of different half cone angles on the flame stabilization, flame front length, and heat exchange efficiency of the burner. The research in this paper provides a reliable direction for the design optimization of low-NOx burners.