The binding energies of the ground and some low-lying excited states of a D− centre in a GaAs/GaAlAs quantum well have been calculated as a function of the presence of an applied magnetic field and well width respectively. In comparison with exact two-dimensional results, which show only four bound states, a larger number of D− bound states appear in a quantum well. Moreover, the critical magnetic field values at which the excited states change from unbound to bound are obtained, and the reasons of the binding energy as function of magnetic field and well width are discussed. Our results are in good agreement with those in the literature.