To improve both driving stability and riding comfortability with respect to vibration input through wheel and damper from road surface.

In a mount structure of damper, a piston rod 12 of the damper is connected to a car body side through a mount 30. The mount 30 has a mount rubber 31 equipped with a car body side attaching section 19, and a shock absorber 40 arranged between the mount rubber 31 and piston rod 12, and the shock absorber 40 of the mount 30 allows the piston rod 12 to be stationary when a small damper load is applied, and allows it to be movable by a fixed stroke when the damper load being a fixed value or more is applied.