This paper aims at developing an anisotropic mesh adaptation strategy for Large Eddy Simulation (LES) of industrial applications. Starting from the Isotropic Automatic Mesh Convergence (IAMC) strategy developed previously and using the anisotropic remeshing methodologies initially developed for RANS, we propose a novel Anisotropic Automatic Mesh Convergence (AAMC) strategy to ensure similar LES accuracy, but with fewer mesh elements than with the IAMC strategy. As with the IAMC strategy, this new strategy is designed to ensure proper mean flow resolution and that enough turbulent scales are resolved in fully turbulent regions to perform reliable LES. However, particular attention is needed to ensure that the primary instabilities leading to the transition to turbulence are correctly accounted for with the anisotropic meshes