A novel after-burner used for the heat-up and normal operating conditions of a metal-supported planar solid oxide fuel cell (SOFC) system, is designed and experimentally studied in this paper. The burner construction and the calculation of maximum burner power are shown in detail. Meanwhile, its static characteristics are researched through the influence of excess air ratio (ER), air velocity, inlet air temperature, and fuel utilization rate (Uf) and its transient characteristics are researched through the processes of burner start-up, burner operating state switch, and stack start-up. The results suggest that the best ER value gets larger with the increased burner power. The air velocity is better controlled within 3 m/s to prevent the influence of a lifted flame. High inlet air temperature can extend the lean combustion range and reduces incomplete combustion products, but large ER mutations should still be avoided. In the case of anode off-gas combusting with cathode off-gas, there are nearly zero emissions. Meanwhile, the flue gas temperature decreases to about 760 °C because of enlarged heat loss, but it is minimally influenced by Uf. Under the static condition, the optimal point with both controlled temperature and lowest emissions can be obtained in a wide range, and the after-burner can well adapt to various operating states of the stack. Under the transient condition, the after-burner has good response performance with much shorter time in burner start-up and burner operating state switch than conventional porous media ones. It can start up the stack in 1715 s.