  We study the superfluidity of a pure spin current that is a spin current
without mass current. We examine two types of pure spin currents, planar and
circular, in spin-1 Bose gas. For the planar current, it is usually unstable,
but can be stabilized by the quadratic Zeeman effect. The circular current can
be generated with spin-orbit coupling. When the spin-orbit coupling strength is
weak, we find that the circular pure spin current is the ground state of the
system and thus a super-flow. We discuss the experimental schemes to realize
and detect a pure spin current.
