The ground state binding energy of axial hydrogenic impurity in GaAs/Ga1-xAlxAs cylindrical quantum well wires (CQWWs) are investigated as a function of the barrier height and the radius of the wire under hydrostatic pressure in the effective mass approximation and variational calculation scheme. The effect of applied hydrostatic pressure is introduced into the calculations using pressure dependent values of energy gap, effective mass and dielectric constant. We have found that for large radii the binding energies are not affected by applied pressure. However, in the region where the particles interact with the barrier the binding energy is strongly dependent on the hydrostatic pressure for all x values. Furthermore, we have shown that this dependency is as strong as the binding energy increase via Al concentration increase. (C) 2010 Elsevier B.V. All rights reserved.