A vibration in a high-speed machine may lead to machinery malfunction and even catastrophic failure. So solving the vibration problem is a fundamental requirement for the stability of the high-speed machine. The flywheel energy storage system using superconducting magnetic bearings is a device to store electrical energy as rotational kinetic energy by motor and to convert it to electrical by generator when necessary. The high-speed rotating flywheel has large amplitude at a critical speed. And it has an unstable behavior by the electric torque at the first stage of the energy generation. In this paper, the stability analysis is performed with an analytical model and equations of motion-which is considered the effect of the electric torque-to identify the stable driving condition and the dynamic behavior.