We introduce a procedure to generate metric-orthogonal anisotropic volume meshes. These meshes are obtained when most of the edges are aligned with the eigenvectors of a provided input metric field. The goal is to generate locally structured meshes in an anisotropic context and in the presence of complex geometries. The algorithm relies on two local mesh modification operators. The first one is used to quickly coarsen volume meshes. From a coarse volume mesh, the second operator is used to insert iteratively points in a frontal manner. The local alignment and orthogonality are naturally inherited from the eigenvectors and eigenvalues of an input metric field. We show on several 3D numerical examples that this procedure is robust and can generate anisotropic locally structured meshes.