We report coherent frequency conversion in the gigahertz range via three-wave mixing in a single artificial atom in open space. All frequencies involved are in the vicinity of transition frequencies of the three-level atom. A cyclic configuration of levels is therefore essential, which we have realized with an artificial atom based on the flux qubit geometry. The atom is continuously driven at two transition frequencies and we directly measure the coherent emission at the sum or difference frequency. Our approach enables coherent conversion of the incoming fields into the coherent emission at a designed frequency in prospective devices of quantum electronics.