The tribological behaviour of articular cartilage is likely to be anisotropic due to the unidirectional alignment of the superficial collagen fibres in the tissue, which yet remains insufficiently explored. The aim of this study was to investigate the effect of fibre orientation in the superficial zone of the articular cartilage on its tribological behaviour. Coefficient of friction (CoF) and wear of bovine cartilage pins that were reciprocally rubbed against cobalt chromium molybdenum discs were measured and analyzed at four angles between the superficial collagen fibre orientation and the sliding direction. A new wear law describing the anisotropic wear behaviour of the cartilage was developed based on the experimental data. The wear depth of the cartilage specimens was minimal when the sliding was in the same direction with the fibres and gradually increased with the increase in the fibre-sliding angle until the sliding direction was perpendicular to the fibre alignment. The CoFs in these wear tests at different fibre-sliding angles remained relatively similar and were not correlated with the wear depth. The wear law fit the experimental results reasonably well. The anisotropic wear behaviour of the cartilage is marked and subject to the unidirectional orientation of the superficial fibres in the cartilage. The proposed anisotropic wear law provides a step forward towards simulation of wear of the cartilage and joints. This study provides insights for the development of osteochondral grafts.