  Spin transport properties of the quantum one-dimensional non-linear sigma
model are studied based upon the Bethe ansatz exact solution for the O(3) sigma
model and the 1/N-expansion approach for the O(N) sigma model. It is shown that
the spin transport at finite temperatures is ballistic and there is no spin
diffusion in this system. A possible mechanism for the spin diffusion observed
in the NMR experiment of the Haldane gap system AgVP_2S_6 by Takigawa et al.
[Phys. Rev. Lett.{\bf 76}, 2173 (1996)] is also discussed. The inclusion of the
spin-phonon interaction accounts for the experimental results qualitatively.
