The invention belongs to the field of nitroxide free radical catalysts, aims at solving the problem that the existing homogeneous catalyst TEMPO (tetramethyl-piperidyl-nitroxide free radical) is difficult to separate and recover after reaction and can not be reused to seriously restrict development of a catalytic system, and provides an epoxy polymer microsphere immobilized (tetramethyl-piperidyl-nitroxide free radical) TEMPO catalyst, as well as a preparation method and an application method thereof. According to the preparation method, 4-OH-TEMPO (4-hydroxy-2,3,6,6-tetramethyl-piperidyl-nitroxide free radical) is bonded on a (crosslinked poly glycidyl methacrylate microsphere) CPGMA to prepare the solid catalyst TEMPO/CPGMA shown in the general formula I immobilized by TEMPO. According to the preparation method, the TEMPO is subjected to chemical bonding on a solid carrier, immobilization of TEMPO is realized, homogeneous catalysis oxidation is changed to heterogeneous catalysis oxidation, and therefore, the heat stability of the catalyst is improved, separation of the catalyst from a reaction medium is convenient, the catalyst is reused, and high activity can be generated.