Energy levels of ground- and excited shallow acceptor states in quantum wells (QWs) have been calculated in the presence of an external magnetic field within a four-band effective-mass theory, in which the valence-band mixing as well as the mismatch of the band parameters and the dielectric constants between well and barrier materials have been taken into account. The energy separations between the ground and different excited acceptor states are deduced at various magnetic fields. The g-factors of the acceptor 1S3/2 ground states and the 2P3/2 excited states are obtained for QWs with different well widths. The oscillator strengths of the acceptor infrared transitions in QWs corresponding to the G, D, and C lines of acceptors in bulk GaAs have also been calculated vs magnetic field up to 10 T.