In a sealing device for a rotary machine of the type that an annular groove is provided in an inner circumferential surface of a through-hole of a stationary member through which a rotary body supported rotatably by a bearing device extends, gap spaces between the rotary body and the both side portions of the stationary member on the opposite sides of the annular groove are sealed by seal rings, and a seal fluid feed hole for feeding a sealing fluid into the annular groove is provided in the stationary member; improvements are made in that a vibration suppressing movable ring is accommodated within the annular groove, the movable ring is mounted to the stationary member so as to be movable only in a radial direction so that an outside annular gap clearance may be formed between an outer circumferential surface of the movable ring and an inner circumferential surface of the annular groove and also an inside annular gap clearance may be formed between an inner circumferential surface of an inner hole of the movable ring and an outer circumferential surface of the rotary body which extends through the inner hole, the inside gap clearance is divided into a plurality of arcuate gap clearance sections, and the respective arcuate gap clearance sections a formed in a wedge-like shape that is gradually narrowed towards the downstream side in the direction of rotation of the rotary body.