In this Letter we analyze the general features of quantum transport in a ferromagnetic nanowire based on a simple model. The local spin distribution, provided by well localized d-electrons, is governed by the Heisenberg-Ising ferromagnetic Hamiltonian while for the s-like conduction electron we have considered the Anderson model. The interaction between local spin and itinerant electrons is given by H-I = -DeltaSigma(i)S(i) (.) sigmadelta(x - x(i)). The conductance formulae and the giant magnetoresistance effect for a nanowire placed between two ferromagnetic electrodes are obtained. (C) 2004 Elsevier B.V. All rights reserved.33414654