Disclosed are a magnetic bearing device with a vibration restraining function, a magnetic bearing device with a vibration estimating function, and a pump device with the magnetic bearing devices mounted thereto, in which it is possible to realize a reduction in vibration in the apparatus system as a whole inclusive of the equipment associated with the vacuum pump without newly providing a vibration sensor. In a vibration detector, a multiplication result obtained by multiplying the Laplace transformation of a displacement of a rotor by a predetermined transfer function is added to a multiplication result obtained by multiplying the Laplace transformation of a variation in an unbalance force acting on the rotor by the reciprocal of the mass of the rotor. The result of this calculation is reversed in polarity and is added to the output of a compensator by an adder.