We present a theoretical study of impurity-related photoluminescence of acceptor-doped GaAs–(Ga,Al)As superlattices under in-plane magnetic fields within the effective-mass approximation. An expansion in terms of sine functions is used in order to obtain electron and hole magnetic Landau levels whereas products of sine and hydrogenic-like variational functions are taken for the shallow-acceptor envelope wave functions. The magnetoluminescence lineshapes associated to transitions from the lowest Landau conduction subband to impurity states are calculated for an homogeneous distribution of acceptors throughout the semiconducting superlattice. We found quite good agreement between the theoretical acceptor-related magnetoluminescence peak positions for GaAs–(Ga,Al)As superlattices and available experimental data.