A divergent porous medium burner with three embedded preheaters has been numerically studied in this paper. The burner can be used to recover heat from Solid Oxide Fuel Cell for burning extremely low calorific off-gas. The developed burner consists of a conical section filled with porous media in the upper part and three preheaters located downstream through which the fresh mixture recovers heat from exhaust gas. A coupled solution method is used to study the structure of the preheater, and the feasibility of the method is verified. The results show that the burner can use the heat recovered from the exhaust gas to burn mixtures without the need for any external heating. The burner is capable of dealing with extremely low calorific off-gas, it can stabilize the combustion of a mixture with a heating value of 0.908 MJ/kg. The results also show that the mass flow ratio has a great influence on the recovery efficiency. When the mass flow ratio is less than one, the recovery efficiency increases sharply with the increase of mass flow ratio. With the further increase of mass flow ratio, the recovery efficiency decreases. This study provides the guidance for the treatment of low-grade off-gas without additional energy consumption.