A series of Be δ-doped GaAs/AlAs multiple-quantum wells with the doping at the well center were grown by molecular beam epitaxy. The photoluminescence spectra were measured at 4, 20, 40, 80, 120, 200 K, respectively. The two-hole transitions of the acceptor-bound exciton from the ground state, 1S 3/2(Γ 6), to the first-excited state, 2S 3/2(Γ 6), have been clearly observed and the acceptor binding energy measured. A variational calculation is presented to obtain the acceptor binding energy as a function of well width. It is found that the experimental results are in good agreement with the theory.