A novel magnetic levitation support method is proposed, which can relieve the perturbation caused by traditional support methods and provide more accurate position control of the capsule. This method can keep the perfect symmetry of the octahedral spherical hohlraum and has the characteristics in stability, tunability and simplicity. It is also favorable that all the results, such as supporting forces acting on the superconducting capsule, are calculated analytically, and numerical simulations are performed to verify these results. A typical realistic design is proposed and discussed in detail. The superconducting coating material is suggested, and the required superconducting properties are listed. Damped oscillation of the floating capsule in thin helium gas is discussed, and the restoring time is estimated.