For the passive vibration isolation system, a friction damper is often used becasue it is sipmle, inexpensive and robust. However, the conventional damper of constant friction force has performance limitations ; the isolation characteristic declines when the friction force is large, while the resonant peak becomes large when the friction force is small. Furthermore, the displacement remains apart from the equilibrium position after the vibration diminishs. In order to overcome above drawbacks of the conventional friction damper, a new type of friction damper is proposed in this paper. In the new friction damper, the friction lever mechanism is devised to make the magnitude of the friction force proportional to the relative displacement. This is achieved by connecting the end of the lever to the restoring spring. The transient response and the displacement transmissibility are examined by numerical simulation and experiments, confirming the effectiveness of the linear friction damper.