  We study the spin-polarized $\nu=0$ Landau-level state of graphene. Due to
the electron-hole attractive interaction, electrons and holes can bound into
pairs. These pairs can then condense into a spin-triplet superfluid ground
state: a spin superconductor state. In this state, a gap opens up in the edge
bands as well as in the bulk bands, thus it is a charge insulator, but it can
carry the spin current without dissipation. These results can well explain the
insulating behavior of the spin-polarized $\nu=0$ state in the recent
experiments.
