The present invention is a method for applying a gradient magnetic field to a paramagnetic supporting liquid containing a mixture of first particles and second particles to separate the mixture by particle type. A magnetic susceptibility of the first particles is lower than that of the liquid, and a magnetic susceptibility of the second particles is higher than that of the liquid. A gradient magnetic field is applied to the liquid in a separation tank provided with a magnetic filter and the liquid is stirred. The first particles float in the liquid by a magneto-Archimedes effect. A horizontal magnetic force acts on the first particles by the gradient magnetic field, so that the first particles travel to a region lateral to or outward from the magnetic filter and are gathered in the region. The magnetic filter is excited by the gradient magnetic field to catch the second particles.