The binding energies of the ground state of both the heavy-hole and light-hole excitons in a GaAs(InulcornerGaulcornerAs) quantum well sandwiched between two semi-infinite AlulcornerGaulcornerAs(InP) layers are calculated as a function of well width in the presence of an arbitray magnetic field. A variational approach is followed using very simple trial wave function. The applied magnetic field is assumed to be parallel to the axis of growth and the binding energies are calculated for a finite value of the height of the potential barrier. The exciton binding energies for a given value of the magnetic field are found to be increased than their values in a zero magnetic field due to the compression of their wave functions within the well with the applied magnetic field.