Raman spectra of internal transitions of shallow Be acceptors confined in the center of multiple-quantum GaAs/AlAs wells were studied. A series of Be δ-doped GaAs/AlAs multiple-quantum wells with doping at the well center and wells widths ranging from 30～200  were grown on (100) GaAs substrates by molecular beam epitaxy. Raman and photoluminescence spectra were measured at 4.2 K respectively. The transitions of Be acceptors from the 1S3/2(Γ6) ground state to the 2S3/2(Γ6) first-excited state were clearly observed in Raman spectra. An iterative shooting algorithm and a variational principle were introduced to obtain the 1～2s transition energy of quantum confined Be acceptors as a function of the well width. It was found that the acceptor transition energy increases with the decreasing of quantum wells widths, and the experimental results are in good agreement with the theoretical calculation.