A rolling with cone-shaped mill, the diameter of which continuously Niaries along the axial direction, has been proposed as a new shear rolling for controlling the texture of an aluminum alloy sheet. In this study, variations in the texture and Lankford value of a 1070 aluminum sheet rolled by the cone-shaped roll were investigated. Rolling with the cone-shaped roll was found to impose intense shear strain at the edges of the specimen, specifically near the surface. The shear directions in the left and right portions of the specimen were opposite to each other. The surface and middle layer of the specimen rolled by the cone-shaped roll and the reference specimen were characterized by a shear texture and typical recrystallization texture components, respectively. Notably, the specimen rolled by the cone-shaped roll exhibited smaller texture intensity than the reference specimen, especially at the surface, and the shear texture-components were observed at relatively deeper positions. As a result of Lankford value measurements, the specimen rolled with the cone-shape roll exhibited a smaller planar anisotropy than the reference specimen and an average Lankford value close to unity, which are likely due to the texture modifications introduced during rolling with the cone-shaped roll.