Using far-infrared time-resolved spectroscopy，we have investigated the effect of quantum-well confinement on the lifetime of shallow acceptor states in GaAs/AlAs multiple quantum wells with Be δ-doping. Low-temperature far-infrared absorption measurements clearly show three principal absorption lines due to transitions of Be acceptor states from the ground state to the first three odd-parity excited states，respectively. It is found that the lifetime of excited states is monotonically reduced with decreasing quantum-well width，from 350 ps in bulk to 55 ps in a 100 ? well. We suggest that the effect of quantum-well confinement on zone-fold acoustic-phonon modes increases the intra-acceptor scattering rate of acoustic-phonon-assisted relaxation.