A vibration-damping component, a gas turbine engine having the vibration-damping component and a method for forming such component are disclosed. The vibration-damping component comprises a body formed from an additive manufacturing material by an additive manufacturing process and defining a cavity within the body, and a vibration damper disposed within the cavity. The vibration damper comprises a damping element and a damping medium containing a viscoelastic material surrounding the damping element. The damping element has a relative motion when the component vibrates.