An apparatus for forming a thin film of a given material on one or more substrates comprises a vacuum vessel, a first electrode which is provided in the vacuum vessel for holding a target plate of the given material thereon, a second electrode which is provided opposite to the first electrode in the vacuum vessel to form a discharge space between the first and second electrodes and holds the substrate(s) thereon, a gas conduit for supplying a sputtering gas into the discharge space, power sources for applying a discharge voltage between the first and second electrodes to generate a discharge plasma of the sputtering gas, and a magnetic field generating device which is provided to surround the discharge space and generates a magnetic field effective to prevent the discharge plasma from diffusing to the outside of the discharge space.