A fixing tool of an auto-tensioner includes inwardly inclined engaging pieces inclined inwardly so as to be opposed to respective tapered surfaces of a spring seat and a cylinder of the auto-tensioner. The engaging pieces have concave surfaces that contact the tapered surfaces over a circumferentially extending area. This minimizes the deformation of the engaging pieces such that the diametrical distances therebetween increase due to contact with the tapered surfaces when sandwiching the spring seat and the cylinder with the engaging pieces from the axially opposite directions, thereby preventing the fixing tool from coming off.