Non-Darcy flow and permeability anisotropy are the essential characteristics of the extra-low permeability reservoir. In order to solve the theoretical calculation problem of areal sweep efficiency for the extra-low permeability anisotropy reservoir，non-Darcy stream tube model was built taking the threshold pressure gradient into account，and the areal sweep efficiency formula and water breakthrough time formula of five-spot well pattern were derived by using of coordinate transformation method to change anisotropy reservoir into an equivalent isotropy reservoir. This method can be used to quantitatively characterize the produced degree of the extra-low permeability anisotropy reservoir by water flooding，and provide theory basis for development and evaluation of the extra-low permeability anisotropy reservoir. Taking an extra-low permeability anisotropy reservoir of Ordos Basin as an example，we analyzed the effect of threshold pressure gradient，permeability anisotropy，well spacing and pressure difference on areal sweep efficiency with this method. The case study shows that when the permeability anisotropy degree is strong，the injected water will preferentially flow along the high permeability direction resulting in the unbalanced development. The adjustment of well spacing and row spacing，the rise of pressure difference and well pattern infilling are effective measures to decrease the dead-oil zone and to increase water flooding swept area.