A macroscopic theory of giant magnetoresistance in granular magnetic materials is developed to improve on that of Rubinstein [Phys. Rev. B 50, 3830 (1994)]. By using a self-consistent method and introducing a useful parametrization, we show the magnetotransport in granular systems to be between those for currents in the plane of layers and currents perpendicular to the plane of the layers in multilayers. The theoretical result in the local limit is found to be in agreement with the observed singular dependence of the giant magnetoresistance on annealing temperature.