I have thought that by eddy current. But how eddy current in superconductivity materials can be generated by using permanent magnet?
As superconductors have zero resistance a large amount of Eddy current flows in them. These eddy currents will generate a magnetic field opposite to that due to the magnet and the repulsion between these magnetic fields is what causes the magnet to levitate.
It is not that it should be a permanent magnet. Levitation works with those which produce a magnetic field like a current carrying coil.