We propose the concept of the spin superconductor (SSC), a counterpart to the charge superconductor. We carry out theoretical study to show the existence of a spin superconductor in a ferromagnetic graphene, in which the spin-polarized electron-hole excitons play the roles of the `Cooper' pairs. We present a BCS-type theory and the Laudau-Ginzburg theory for the SSC. With the ``London-type equations" of the super-spin-current density, we show the existence of an electric ``Meissner effect" against a spatial varying electric field. We further study a SSC/normal conductor/SSC junction and predict a spin-current Josephson effect. Recent experimental results showing the possible sign of a spin superconductor will also be reported. Some aspect of the electric dipole superconductor will also be discussed.