An auto-tensioner comprising: a cylinder having a closed end; a rod axially movably inserted in the cylinder and having a protruding end protruding beyond the cylinder; a hydraulic damper mechanism configured to dampen a pushing force applied to the rod; a spring seat fixed to the protruding end of the rod; a return spring configured to bias, through the spring seat, the rod in a direction in which the rod protrudes out of the cylinder; and a fixing tool (40, 50) configured to be fitted to outside of the cylinder and the spring seat so as to keep the rod pushed into the cylinder, wherein the spring seat includes a flange supporting the return spring, and a coupling piece axially protruding from the flange, wherein the cylinder includes a coupling piece axially protruding from the closed end of the cylinder, and wherein at least one of the spring seat and the cylinder has a tapered surface (31, 16) having a diameter which decreases axially toward the coupling piece (26, 15) of the at least one of the spring seat and the cylinder; characterized in that the fixing tool (40, 50) includes: a pair of side portions (42 and 43) defining a partial circumferential opening therebetween, and arranged so as to sandwich the cylinder and the spring seat in a diametrical direction; and a connecting portion circumferentially connecting the pair of side portions (42 and 43) together at a position opposite from the partial circumferential opening, wherein each of the pair of side portions (42 and 43) includes a first engaging piece (45, 46) and a second engaging piece (45, 46) that are configured to sandwich the cylinder and the spring seat from axially opposite directions with the first engaging piece (45, 46) opposed to the tapered surface (31, 16), the first engaging piece (45, 46) being inclined inwardly and having a concave surface (47, 48) configured to contact the tapered surface (31, 16) over a circumferentially extending area. a cylinder having a closed end; a rod axially movably inserted in the cylinder and having a protruding end protruding beyond the cylinder; a hydraulic damper mechanism configured to dampen a pushing force applied to the rod; a spring seat fixed to the protruding end of the rod; a return spring configured to bias, through the spring seat, the rod in a direction in which the rod protrudes out of the cylinder; and a fixing tool (40, 50) configured to be fitted to outside of the cylinder and the spring seat so as to keep the rod pushed into the cylinder, wherein the spring seat includes a flange supporting the return spring, and a coupling piece axially protruding from the flange, wherein the cylinder includes a coupling piece axially protruding from the closed end of the cylinder, and wherein at least one of the spring seat and the cylinder has a tapered surface (31, 16) having a diameter which decreases axially toward the coupling piece (26, 15) of the at least one of the spring seat and the cylinder; characterized in that the fixing tool (40, 50) includes: a pair of side portions (42 and 43) defining a partial circumferential opening therebetween, and arranged so as to sandwich the cylinder and the spring seat in a diametrical direction; and a connecting portion circumferentially connecting the pair of side portions (42 and 43) together at a position opposite from the partial circumferential opening, wherein each of the pair of side portions (42 and 43) includes a first engaging piece (45, 46) and a second engaging piece (45, 46) that are configured to sandwich the cylinder and the spring seat from axially opposite directions with the first engaging piece (45, 46) opposed to the tapered surface (31, 16), the first engaging piece (45, 46) being inclined inwardly and having a concave surface (47, 48) configured to contact the tapered surface (31, 16) over a circumferentially extending area. a pair of side portions (42 and 43) defining a partial circumferential opening therebetween, and arranged so as to sandwich the cylinder and the spring seat in a diametrical direction; and a connecting portion circumferentially connecting the pair of side portions (42 and 43) together at a position opposite from the partial circumferential opening, wherein each of the pair of side portions (42 and 43) includes a first engaging piece (45, 46) and a second engaging piece (45, 46) that are configured to sandwich the cylinder and the spring seat from axially opposite directions with the first engaging piece (45, 46) opposed to the tapered surface (31, 16), the first engaging piece (45, 46) being inclined inwardly and having a concave surface (47, 48) configured to contact the tapered surface (31, 16) over a circumferentially extending area.