An excitonic magnet hosts a condensate of spin-triplet excitons composed of conduction-band electrons and valence-band holes and may be described by the two-orbital Hubbard model. When the Hamiltonian has the nearest-neighbor interorbital hopping integrals with d-wave symmetry and the number of electrons is slightly away from half filling, the k-space spin texture appears in the excitonic phase with a broken time-reversal symmetry. We then show that, applying electric field to this doped excitonic magnet along a particular direction, a pure spin current emerges along its orthogonal direction. We discuss possible experimental realization of this type of the pure spin current in actual materials.
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