In the effective-mass approximation, using a simple two-parameter wave function and a one-dimensional (1D) equivalent potential model, we calculate variationally the binding energy of an exciton bound to a neutral donor (D0,X) in finite GaAs-AlxGa1−xAs quantum well wires (QWWs). At the wire width of 25 A, the binding energy has a peak value, which is also at the position of the peak of the exciton binding energy, and the center-of-mass wave functions of excitons reaches the most centralized distribution. In addition, the changing tendency of the average interparticle distance as the wire width is reverse to that of the binding energy.