A magnetron sputtering apparatus of the invention includes: a sputtering chamber in which a target can be opposed to an object to be subjected to film formation; a gas introduction port facing the sputtering chamber; a magnet provided outside the sputtering chamber and opposite to the target and being rotatable about a rotation center which is eccentric with respect to center of the magnet; a sensor configured to detect a circumferential position of the magnet in a plane of rotation of the magnet; and a controller configured to start voltage application to the target to cause electrical discharge in the sputtering chamber on the basis of the circumferential position of the rotating magnet and gas pressure distribution in the sputtering chamber.