Recently, the so-called room-temperature ferromagnetism in any nanoparticles has been studied intensively. It is well known that the properties of ferromagnetism and superconductivity are contradictory in a superconducting high-Tc cuprate. The existence of ferromagnetism in the nanoparticles has been suggested to occur on the surface. This magnetism has been expected to come from defects inducing magnetic moments on oxygen vacancies at the surface of the nanoparticles. This work is to observe magnetism in nanosized superconducting Pr2-xCexCuO4 (PCCO) with x = 0.15 by means of a superconducting quantum interference device (SQUID). The magnetization curves of the reduced PCCO nanoparticles with the superconducting transition temperature, Tc, of ~25 K have revealed that there is weak ferromagnetism observed at room temperature. The magnitude of magnetization could be enhanced by oxygen reduction annealing in vacuum with increasing annealing temperature. A non-linear magnetization occurring in the reduced PCCO nanoparticles through the vacuum annealing process is probably due to a strong oxygen reduction producing more oxygen vacancies in the T'-structure.