Sedimentary and diagenetic processes usually make reservoirs anisotropic. The existing anisotropy studies mainly focus on the absolute permeability of reservoirs, but lack of studies on relative permeability anisotropy, which cannot reflect the difference of interference degree between fluid phases in different directions. In order to study the effect of an anisotropic structure on oil-water two-phase seepage, a three-dimensional staggered coring method was designed to reduce the influence of end effects in conventional cubic core anisotropy relative permeability experiments, and a method to obtain an anisotropic relative permeability curve was established. On this basis, an anisotropy experiment of oil-water relative permeability of natural sandstone is carried out, which proves the existence of anisotropy of relative permeability of sandstone reservoirs. The generation mechanism and tensor expression of anisotropic relative permeability are analyzed. The effect of relative permeability anisotropy on seepage processes is studied. The results show that bedding structure is the main cause of relative permeability anisotropy of sedimentary reservoirs. Relative permeability anisotropy quantifies the difference of water-phase coning ability and water-oil fluidity ratio in different directions. The relative permeability curve in the high permeability direction is characterized by high residual oil saturation, a narrow two-phase seepage zone, low water saturation and low relative permeability at the isotonic point. Relative permeability anisotropy will lead to oil and water seepage, which will have a significant impact on reservoir development. As the development process progresses, oil and water seepage directions will gradually show obvious differences, and one-way dead oil zones and plane dead oil zones appear successively, resulting in a more complex distribution of remaining oil.