The Solid Oxide Fuel Cell (SOFC) system is characterized by high energy conversion efficiency and low emissions. The energy supply and recovery of the SOFC system are facilitated through the ignition burner and the off-gas burner, respectively. This study proposes a coupled design of the ignition burner and the off-gas burner to reduce the burner volume, thereby enhancing the power density of the SOFC system. The ignition burner employs radially opposed jet combustion with fully premixed natural gas, while the off-gas burner uses swirl diffusion combustion with the anode off gas. When the premixed gas and lean anode off gas are unable to sustain the flame, catalytic combustion is initiated. Simulation and experiment methods are utilized to analyze the performance of the coupled burner in this paper. The results indicate that uniform mixing is achieved with a high swirl number (s1 = 2.6) for the premixed gas, and the maximum excess air coefficient for stable flame combustion at 400 °C is 2.47. As the temperature of the cathode off gas increases, the flameout boundary for the premixed gas gradually increases; conversely, with increasing burner power, the flameout boundary gradually decreases. The intersection cooling effect of mixed air and circumferential high-temperature flue gas is effective, and the flame does not exceed the tolerance temperature of the catalytic carrier. The diffusion combustion of anode off gas with a swirl number (s2 = 0.5) exhibits great gas mixing uniformity without a high-temperature core region. When transitioning from flame to catalytic combustion with premixed natural gas and anode off gas, there is a temperature lag of approximately 60 s. The isotropic cylindrical cordierite catalytic carrier with a 400 mesh and a coating of 60 g/ft3 Pt0.1Pd0.5 achieves stable catalytic combustion in an environment with preheated air temperatures ranging from 400 to 600 °C and H2 concentrations of 0.25–2.91 %.