Photoluminescence of shallow Be acceptors in both bulk GaAs and a series of δ-doped GaAs/AlAs multiple quantum well samples with well width range from 30 to 200　? were studied. A series of Be δ-doped GaAs/AlAs multiple quantum wells with the doping at the well center and a single epilayer of GaAs uniformly Be doped were grown by molecular beam epitaxy. The photoluminescence spectra were measured at 4.2 K. The two-hole transition of the acceptor-bound exciton from the ground state, 1s3/2（Γ6）, to the first-excited state, 2s3/2（Γ6）, have been clearly observed. A variational principle is used to obtain the 2s-1s transition energy of quantum confined Be acceptors as a function of the well width. It is found that the acceptor transition energy increases with decreasing quantum well width, and the experimental results are in good agreement with the theoretical calculation.