A calculation is presented of spontaneous radiation emitted by an electron beam passing through a continuously rotating quadrupole magnetic undulator. It is shown that radiation spectrum emitted in forward direction of beam propagation has four peaks, corresponding to four betatron frequencies. Utilizing the Madey theorem, a stimulated emission is calculated and presented as gain versus frequency curves, for different values of the quadrupole magnetic field. A free‐electron laser operating at two or three radiation frequencies with a quadrupole magnetic wiggler is suggested.