The icephobic materials induced using micro-nano-structured surfaces have aroused great attention for promising applications. Previously, the characterization of ice adhesion of icephobic materials by shear force is usually performed without direction discrimination along the surface whatever the surface is anisotropic or not. In this work, we studied the direction-dependent ice adhesion strength on groove-shaped micro-nano-structured aluminum alloy surfaces formed using a femtosecond laser. It is found that the ice adhesion strength on the surfaces exhibits anisotropy, which corresponds to a smaller ice adhesion strength in the direction parallel to the groove than that orthogonal to the groove. Furthermore, it is found that the ice adhesion strength decreases with the increase in groove width in the orthogonal direction, while it does not change much in the parallel direction. The anisotropic ice adhesion strength is attributed to the change of wettability and morphology in the two directions. The findings in this work suggest that anisotropic ice adhesion should be fully considered when designing an icephobic micro-nano-structured metal structure, which is of great significance to the characterization and application of icephobic materials.