Exciton binding energies of heavy- and light-hole excitons affected by charge-carrier screening in GaAs-AlxGa1-xAs quantum wells are calculated by the variational-perturbation method. The exciton binding energies are found to decrease rapidly when the screening length is less than 30aBh (effective exciton Bohr radius). This screening length corresponds to a carrier density of 7.0×1013/cm3 at T=10 K. In the calculation, the Debye screening model is used for charge carriers. The exciton binding energies as functions of the screening length, carrier density, and quantum-well parameters have been calculated. The critical carrier densities, above which no excitons can be formed, are obtained at different well thickness. The effects of charge-carrier screening to the exciton photoluminescence are also discussed.