A superconductor comprising a compound of the formula (II):R.sub.1+x Ba.sub.2-x Cu.sub.3 O.sub.7-y1 (II)wherein not less than 40% of a crystal of the superconductor shows phase separation, and at (temperature, magnetic field) of (77�K!, O�T!) and (77�K!, 4�T!), a critical current density is not less than 10,000 A/cm.sup.2, which is obtained by heating a precursor which is a solid solution of the formula (I):R.sub.1+x Ba.sub.2-x Cu.sub.3 O.sub.7-y (I)wherein not more than 10% of a crystal of the solid solution shows phase separation, so that phase separation is formed in the crystals at a phase separation temperature, and introducing oxygen; and a superconductor comprising a compound of the formula (II):R.sub.1+x Ba.sub.2-x Cu.sub.3 O.sub.7-y1 (II)wherein not more than 10% of a crystal of the superconductor shows phase separation, and in a magnetic field of not less than 1�T! at a constant temperature of 77�K!, a critical current density is less than 10,000 A/cm.sup.2, which is obtained by introducing oxygen into the precursor (I) at a temperature less than the lower limit of the phase separation temperature. According to the method of the present invention, a superconductor having a high Jc or having different properties with respect to Jc, which is unobtainable by the conventional production method, can be obtained using the conventional materials.