From the technological point of view, the levitation force is of great importance in the use of high-temperature superconductor (IITSC). In this context, RE3(Y, Nd, Sin, Gd)fia5CusOy (RE-358) hulk HTSCs were fabricated using Solid-State Reaction and Melt-Powder-Melt-Growth (MPMG) techniques. The measurement of levitation force of FITSCs was performed with a developed closed-cycle cryostat levitation system. The measurements were carried out at 33 K in the zero field-cooled regime. The magnetic field of permanent magnet changes exponentially in accordance with the vertical axis, and its value in the closest distance to-RISC is 3392 G. The highest repulsive force which is 3634 niN belongs to the Y-358 MPMG at 33 K. The highest attractive three which is-277 mN belongs to the Nd-358 MPMG at 33 K. Thus, it has been determined that the levitation force of new RE-358 IITSC is better than that of conventional RE-123 IITSC. The results of this study will be beneficial to the future studies on RE-358.