The effect of quantum confinement on the shallow acceptor transition in δ-doped GaAs/AlAs multiple-quantum wells with a width of 30A～200A is studied by using photoluminescene spectra. The samples used in the experiment are the Be δ-doped GaAs epilayers grown by molecular beam epitaxy (MBE) and a series of GaAs multiple-quantum wells in the center of which shallow acceptor Be are δ-doped. The photoluminescene spectra of the samples are measured at a low temperature of 4.2K and the two-hole transition of the acceptor-bound exciton from the ground state, 1S3/2(Γ6), to the excited states, 2S3/2(Γ6) and 3S3/2(Γ6), are observed clearly. It is found that the transition energy of acceptors increases with the enhancement of quantum confinement. The study of the quantum confinement effect used to tune the transition energy of acceptor states has further enhanced the understanding of the acceptor states and has provided a new way to develop terahertz far infrared light emitters or lasers.