We have measured the thermal conductivity along the [101] direction, κ[101], along the [101] direction, κ[101̄], and along the b-axis, κb, of the quasi one-dimensional S=1/2 spin system Sr2V3O9 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 [101] direction. It has been found that both κ[101], κ[101̄] and κb show one peak around 10 K in zero field and that the magnitude of κ[101̄] is larger than those of κ[101] and κb. By the application of magnetic field along the heat current, the peak of κ[101̄] is markedly suppressed, while the peaks of κ[101] and Kb little change. These results indicate that there is a large contribution of spinons to κ[101̄] and suggest that the spin-chains run along the [101] direction.