Active magnetic bearings and superconducting magnetic bearings were used on a high-speed flywheel energy storage system; however, their wide industrial acceptance is still a challenging task because of the complexity in designing the elaborate active control system and the difficulty in satisfying the cryogenic condition. A hybrid bearing consisting of a permanent magnetic bearing and a pivot jewel bearing is used as the support for the rotor of the energy storage flywheel system. It is simple and has a long working life without requiring maintenance or an active control system. The two squeeze film dampers are employed in the flywheel system to suppress the lateral vibration, to enhance the rotor leaning stability, and to reduce the transmitted forces. The dynamic equation of the flywheel with four degrees of complex freedom is built by means of the Lagrange equation. In order to improve accuracy, the finite element method is utilized to solve the Reynolds equation for the dynamic characteristics of the squeeze film damper. When the calculated unbalance responses are compared with the test responses, they indicate that the dynamics model is correct. Finally, the effect of the squeeze film gap on the transmitted force is analyzed, and the appropriate gap should be selected to cut the energy loss and to control vibration of the flywheel system.