A new foil bearing, ViscoElastic Foil Bearing(VEFB) is suggested with the need for a high damping foil bearing. Sufficient damping capacity is a key technical hurdle to super-bending-critical operation as well as widespread use of foil bearings into turbomachinery. The super-bending-critical operation of the conventional bump foil bearing and the VEFB is examined, as well as the structural dynamic characteristics. The structural dynamic test results show that the equivalent viscous damping of the VEFB is much larger than that of the bump bearing, and that the structural dynamic stiffness of the VEFB is comparable or larger than that of the bump bearing. The results of super-bending-critical operation of the VEFB indicate that the enhanced structural damping of the viscoelastic foil dramatically reduces the vibration near the bending critical speed. With the help of increased damping resulting from the viscoelasticity, the suppression of the asynchronous orbit is possible beyond the bending critical speed.