A magnetically levitated vibration damping apparatus includes a table (11) having a flat board of a magnetic material, an electromagnetic actuator (12) for applying magnetic attractive forces to the flat board to levitate the table (11), a displacement sensor (14) for detecting relative displacement between the flat board and the electromagnetic actuator (12), an acceleration sensor (13) for detecting absolute acceleration of the table (11), and a control system (15) for controlling a current supplied to the electromagnetic actuator (12) based on signals from the displacement sensor (14) and the acceleration sensor (13) according to a first control rule for controlling a gap (Z) between the flat board and the electromagnetic actuator (12) based on the signal from the acceleration sensor (13) and a second control rule for controlling vibrations of the table (11) based on the signal from the acceleration sensor (13), the second control rule including stability control (15) of relative displacement of the table (11).