An exhaust gas bypass device comprising: an actuator which reciprocates a driving rod in an axial direction; a connection rod which is connected to a distal end portion of the driving rod; a support shaft which is rotatably supported by a support tube; a connection link whose one end portion is rotatably connected to a distal end portion of the connection rod via a connection shaft and the other end portion is fixed to one end portion of the support shaft; and a waste gate valve which is connected to the other end portion of the support shaft; and a damping member which attenuates a displacement between the connection rod and the connection link; wherein the damping member is an extension portion of the connection link in a longitudinal direction of the connection rod; and the connection rod and the extension portion of the connection link are in sliding-contact with each other; characterized in that a first length of the connection link at a connection portion between the connection link and the connection rod in a longitudinal direction of the connection rod is set to be longer than a second length of the connection link at a fixed portion between the connection link and the support shaft in the longitudinal direction of the connection rod; and wherein when an axial length of the support tube is defined as L3, a radial gap between an outer peripheral surface of the support shaft and an inner surface of the support tube is defined as d, an axial gap of the connection shaft between the connection link and the connection rod is defined as S, and a length of the connection link from a center position of the connection shaft to an end portion in a longitudinal direction of the connection rod is defined as L1, d/L3 > S/L1 is satisfied. an actuator which reciprocates a driving rod in an axial direction; a connection rod which is connected to a distal end portion of the driving rod; a support shaft which is rotatably supported by a support tube; a connection link whose one end portion is rotatably connected to a distal end portion of the connection rod via a connection shaft and the other end portion is fixed to one end portion of the support shaft; and a waste gate valve which is connected to the other end portion of the support shaft; and a damping member which attenuates a displacement between the connection rod and the connection link; wherein the damping member is an extension portion of the connection link in a longitudinal direction of the connection rod; and the connection rod and the extension portion of the connection link are in sliding-contact with each other; characterized in that a first length of the connection link at a connection portion between the connection link and the connection rod in a longitudinal direction of the connection rod is set to be longer than a second length of the connection link at a fixed portion between the connection link and the support shaft in the longitudinal direction of the connection rod; and wherein when an axial length of the support tube is defined as L3, a radial gap between an outer peripheral surface of the support shaft and an inner surface of the support tube is defined as d, an axial gap of the connection shaft between the connection link and the connection rod is defined as S, and a length of the connection link from a center position of the connection shaft to an end portion in a longitudinal direction of the connection rod is defined as L1, d/L3 > S/L1 is satisfied.