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This is the report clarifying the orientation dependence of the wear behavior of Co–Cr–Mo alloy. The wear resistance of the Co–Cr–Mo alloy with face-centered cubic (fcc) structure was found to be higher on the planes in order of {110}, {001} and {111}. Quantitatively, the wear resistance on {110} is 1.5 times larger than that on {111}. The tendency showed in coincident with the orientation dependence of the surface hardness, as empirically suggested. However, we additionally found in the observation of the worn surface in the fcc-single crystals that the volume fraction of the hexagonal close-packed (hcp)-phase, which was formed as the strain-induced martensite during the wear test, was larger in the same order of the wear resistance. The variation in formation frequency of the hcp-phase during the wear test can be explained by focusing on the Schmid factor along the resultant direction of the applied stress and the friction stress. On the {111} surface where the Schmid factor for the strain-induced ε-martensite formation is small, homogeneous deformation microstructure covered by it was not developed even after long-time wear, resulting in lower wear resistance. The results strongly suggest that not only the hardness, but the distribution of the ε-martensite is important to control the wear behavior of the Co–Cr alloys with the extremely low stacking fault energy, and it can be achieved by the crystal orientation control in the γ-phase. [Display omitted] • Orientation dependence of the wear behavior of Co–Cr–Mo alloy was first clarified. • Quantitatively, the wear resistance on {110} is 1.5 times larger than that on {111}. • Strain-induced hcp-phase martensite formation behavior strongly affects the wear resistance. • Design of novel "single-crystalline implant" with much superior properties is expected. [ABSTRACT FROM AUTHOR]