Phonon fluorescence in semiconductor quantum wells induced by two radiation fields is investigated here. The rate of change of the interface LO-phonon population due to the scattering of confined electrons in the two laser fields is calculated using first-order perturbation theory from which the amplification coefficient is derived. It was found, by considering the full photon absorption and emission processes of laser fields that for a semiconductor quantum well at arbitrary temperature, interface LO phonons propagating parallel to the direction of polarization of the external fields may be amplified over a relatively broad band of phonon wavenumber. An application is made for a GaAs/AlGaAs quantum well system.