The magnetoresistance (MR) of a GeSi nanowires (NWs) array is studied as a function of magnetic field, B, and temperature. We observe an asymmetrical MR versus B with a minimum MR at Bmin ≠ 0. Moreover, Bmin increases with temperature, and is larger for a current perpendicular to the NWs than one parallel. A model is proposed to explain this anomalous MR based on the spin-orbit coupling of holes, which is associated with the band structure and morphology of GeSi NWs. By analyzing the MR around Bmin, considerably different mobilities for holes of different spin orientations are derived.