The present invention provides a damper of an elevator car, a control method of the damper, and an elevator system, belonging to the technical field of elevators. The damper of the present invention includes a base, a clamping mechanism mainly including two clamp arm components, a solenoid drive part, and a link transmission component, wherein the link transmission component is configured to be movable in a direction approximately perpendicular to a guide surface and drive at least one of the two clamp arm components connected thereto to move towards a guide rail. The control method of the present invention can enable the damper to work in a disengaged state, a slight contact state or a damping output state.