We have calculated the binding energy for the ground state of a heavy-hole exciton in GaAs/Ga0.7Al0.3As cylindrical quantum well wires (CQWWs) under the action of a hydrostatic pressure, temperature and magnetic field. The calculations are made using variational methods and the effective mass approximation for a finite confinement potential. The hydrostatic pressure, temperature and magnetic field effects can be summarized as follows; excitonic binding energy is a decreasing function of temperature for fixed pressure and magnetic field also is an increasing function of pressure for fixed temperature and magnetic field values depending on the applied pressure range. For larger magnetic field strengths, the binding energies get larger for any hydrostatic pressure and temperature values as expected. (C) 2013 Elsevier Ltd. All rights reserved.