The anomalous behavior of magnetoresistance has been revealed in a number of granular microwires. In contrast to the giant magnetoresistance of granular alloys, which is associated with the spin-dependent scattering in the bulk of grains and at their surface, is linear in the square of the magnetization, and decreases with an increase in temperature, the magnetoresistance, for example, in Co10Cu90 microwires is negative, increases with an increase in temperature below the Curie temperature, and does not reach saturation in the field dependence in the high-field range. A simple mechanism of negative giant magnetoresistance due to scattering of spin-polarized charge carriers by impurity magnetic moments localized in the nonmagnetic intergranular spacers has been proposed taking into account that a considerable part of magnetic ions in microwires exhibiting this behavior is dissolved in the intergranular spacers. It has been shown that the corresponding contribution to magnetoresistance can reach 10–20%.