  We have measured the thermal conductivity along the [101] direction,
kappa_[101]_, along the [10-1] direction, kappa_[10-1]_, and along the b-axis,
kappa_b_, of the quasi one-dimensional S=1/2 spin system Sr_2_V_3_O_9_ in
magnetic fields up to 14 T, in order to find the thermal conductivity due to
spinons and to clarify whether the spin-chains run along the [101] or [10-1]
direction. It has been found that both kappa_[101]_, kappa_[10-1]_ and kappa_b_
show one peak around 10 K in zero field and that the magnitude of kappa_[10-1]_
is larger than those of kappa_[101]_ and kappa_b_. By the application of
magnetic field along the heat current, the peak of kappa_[10-1]_ is markedly
suppressed, while the peaks of kappa_[101]_ and kappa_b_ little change. These
results indicate that there is a large contribution of spinons to kappa_[10-1]_
and suggest that the spin-chains run along the [10-1] direction.
