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One of the prospective applications of high critical temperature superconductors is a superconducting magnet for the magnetically levitated (Maglev) train. Development shows that RE (rare earth) BaCuO and LRE (light rare-earth) BaCuO superconductors prepared by melt processes have a high critical current density at 77 K and high magnetic fields. LRE-Ba-Cu-O bulk superconductors melt-processed in a reduced oxygen atmosphere, named oxygen-controlled-melt-growth (OCMG) process, are very promising for high field application as a superconducting permanent magnet with liquid nitrogen refrigeration. Compared to good quality melt-grown REBaCuO bulks, LREBaCuO bulks exhibit larger critical current densities in high magnetic fields and much improved irreversibility field at 77 K, implying that more effective flux pinning can be realized in a commercially feasible way. In this study, we discuss the possibility of a superconducting bulk magnet for a Maglev train. A preliminary design of the bulk magnet and also melt processing for REBaCuO and LREBaCuO bulk superconductors and their characteristic superconducting properties are presented.