We use in this paper the variational method to calculate the polarizability of a hydrogenic donor impurity, in the presence of electric field, in a V-groove GaAs/Al(x)Ga(1-x)As quantum wire. The carrier ground states are analytically obtained by an effective potential scheme together with a suitable coordinate transformation that allows the decoupling of the two-dimensional Schrodinger equation. According to the results obtained from the present work for polarizability and binding energy reveals that the impurity position and field direction play important roles. (C) 2009 Elsevier B.V. All rights reserved.