Various embodiments include a trapped vortex combustor and a method for operating trapped vortex combustor. In one embodiment, the trapped vortex combustor comprises a trapped vortex combustion zone and at least one secondary combustion zone disposed downstream of the trapped vortex combustion zone. The trapped vortex combustion zone is operable to receive and combust a first fuel and a first air and produce a first combustion product flowing toroidally therein. The at least one secondary combustion zone is operable to receive and combust the first combustion product and at least one second injection consisting of fuel and/or air and produce at least one second combustion product therein. The combustor may reduce the residence time of the highest temperature combustion products and achieve the lower NOx emission.