The superlattices Fe/Si exhibit an antiferromagnetic coupling for very thin Si layers and giant magnetoresistance (GMR) is observed accompanying this coupling. The GMR for these superlattices measured with a current in the plane of the sample (CIP-GMR) is usually less than 0.2%. Considering a shunt effect due to large resistivity of Si layers, we measured the GMR with a current perpendicular to the sample plane (CPP-GMR). The thickness and width of the electrodes for the CPP measurement were carefully designed so that the current is always homogeneous in the sample. As a result, CPP-GMR for these superlattices is found to be about 3-6 times larger than CIP-GMR. Although a careful design of the electrodes is needed for homogeneity of the current, the technique is much easier than the CPP measurement for metal/metal superlattices and expected to provide valuable information on the spin-dependent electron transport phenomena in the Fe/Si superlattices.