A method for producing an REBaCuO oxide superconductor having large magnetic levitation force, where RE is a rare earth element selected from the group consisting of Y, Sm, Eu, Gd, Dy, Ho, Er, and Yb, involves the steps of using a raw material mixture as the starting feed, heating the raw material mixture for partial melting, followed by cooling and solidification, pulverizing and mixing the resulting solid, shaping the resulting mixture into a given shape, placing or embedding nucleates on or in the resulting shape, followed by heating for partial melting, and cooling the resulting partial melt to a substantial temperature at which a superconducting phase starts to form, followed by slow cooling, whereby the superconducting phase is preferentially formed and grown from a nucleation site.