Using a two-parameter wave function, we calculate variationally the binding energy of an exciton bound to an ionized donor impurity (D+, X) in GaAs-AlxGa1−xAs quantum wells for the values of the well width from 10 to 300A, when the dopant is located in the center of the well and at the edge of the well. The theoretical results confirm that the previous experimental speculation proposed by Reynolds et al. [Phys. Rev. B 40, 6210 (1989)] is the binding energy of D+, X for the dopant at the edge of the well. In addition, we also calculate the center-of-mass wave function of the exciton and the average interparticle distances. The results are discussed in detail.