A kind of microwave power source, called a free‐electron laser (FEL) afterburner, that consists of a free‐electron laser buncher and a slow‐wave output structure sharing a magnetic wiggler field with the buncher is proposed. The buncher and the slow‐wave structure can operate in either a traveling‐wave state or a standing‐wave state. In the buncher, the wiggler field together with the radiation field makes an electron beam bunched, and in the slow‐wave structure the wiggler field keeps the beam bunched while the bunched beam interacts strongly with the slow‐wave structure and thus produces rf power. The bunching process comes from the free‐electron laser mechanism, and the generating process of rf power is in a slow‐wave structure. A three‐dimensional, time‐dependent code is used to simulate a particular standing‐wave FEL afterburner and it is shown that rf power of up to 1.4 GW at 17.12 GHz, can be obtained from a 1 kA, 5 MeV electron beam with an energy spread of less than 1% and an emittance of less than 0.5×10−3&pgr; rad m.