Superconducting flywheel energy storage systems using superconducting magnetic bearings have been studied regarding the possibility of contributing to daily load leveling. To make the system feasible for practical application, the levitation force of the radial-type superconducting magnetic bearing must be enhanced. Therefore, we have come up with an idea to change the shape of the cross sections of the permanent magnet and yoke from the present rectangular form to a trapezoidal (or triangular) shape. We analyzed the levitation force in the case where such a permanent magnet and yoke are applied, and produced and actually measured the permanent magnet and yoke. Moreover, anticipating that the adopting the conventional Y superconductor assembly and Gd superconductor assembly, which has better characteristics than the former, would have an effect on levitation force enhancement, we produced these two types of superconducting bearing assemblies and actually measured them. We demonstrate that levitation force is enhanced when the permanent magnet assembly has a trapezoidal cross section and the Gd superconducting bearing assembly is used.