With increasing shear strain, initially homogeneously distributed melt can segregate into an array of melt-rich bands, flanked by melt-poor regions. To address how the formation of these melt-rich bands affects the transport properties of partially molten rocks, I analyzed X-ray synchrotron microtomographic images of an aggregate composed of 10 vol% basaltic melt and 90 vol% olivine that was sheared to a total strain of 13.3. At 0.16 m per pixel, the spatial resolution of the microtomographic dataset is sufficiently high for quantitative characterization of 3-dimensional melt distribution. The results show that the melt distribution is bimodal: in the melt-poor regions, the total melt fractions range from 0.078-0.100, with no interconnected melt; in the melt-rich regions, the total melt fractions range from 0.116 to 0.178, with the interconnected melt fraction ranging from 0.08 to 0.16. The permeability of the sample was calculated using a digital rock physics approach. Along a melt-rich band, permeability (k) as function of melt fraction (ϕ) and grain size (d) can be expressed as k=(ϕ^3.2 d^2)/12.4. Between melt-rich bands, the permeability is negligible. Thus, the permeability of the sheared partially molten rock is highly anisotropic and negligible in the direction perpendicular to the bands. Grain size measurements were obtained through electron backscatter diffraction. After adjusting for grain size, the permeability of a sheared partially molten rock measured along the direction of melt bands is higher than that of its isotropic counterpart with the same bulk melt fraction. The strong anisotropic permeability provides new insight into the effect of melt band formation on melt migration and melt focusing at mid ocean ridges.