A one-way clutch is proposed which is low in surface pressures and durable. It includes an inner ring having a cylindrical outer surface, and an outer ring having a cylindrical inner surface defining a wedge-shaped space in cooperation with the cylindrical outer surface of the inner ring. A ring-shaped wedge member is disposed in the wedge-shaped space. The wedge member is formed with a cylindrical outer surface and a cylindrical inner surface having a center of curvature that is radially offset from the center of curvature of the cylindrical outer surface of the wedge member. A resilient member is provided between the inner ring and the wedge member to bias the wedge member in a direction to be wedged into the narrow portion of the wedge-shaped space. When the inner ring is rotated in one direction, the wedge member will be brought into wedging engagement with the cylindrical surfaces of the inner and outer rings. Torque is thus transferred from the inner ring to the outer ring.