We have presented the behavior of a shallow donor impurity with binding energy in cylindrical-shaped GaAs/Ga(0.7)Al(0.3)As quantum well wires under high hydrostatic pressure values. Our results are obtained in the effective mass approximation using the variational procedures. In our calculations, we have not considered the pressure related Gamma-X crossover effects. The hydrostatic pressure dependence on the expectation value of ground state binding energy is calculated as a function of wire radius at selected temperatures. We have also discussed the effects of high hydrostatic pressure and temperature on some physical parameters such as effective mass, dielectric constant, and barrier height. A detailed analysis of these calculations has proved that the effective mass is the most important parameter, which explains the dependency of donor impurity binding energies on the high hydrostatic pressure values. (C) 2011 Elsevier B.V. All rights reserved.