The substitutional solute atom induced local lattice distortion (LLD) in dilute metal solid solution was believed to be uniform because the solute atom was supposed to occupy the high symmetry lattice site without breaking the point group symmetry of the crystal lattice. Contrary to this conventional picture, we report in this paper that substitutional Mo atom in Ti-Mo solid solution occupies an off-center position instead of the high symmetry lattice site and leads to highly non-uniform LLD, as evidenced by our first principles calculations. The physics underlying the off-center occupation and non-uniform LLD are shown to be the Jahn-Teller splitting of the degenerated d states of Mo atom. With which, the solid-solutions suffering from non-uniform LLD are predicted. The non-uniform LLD challenges the application of classical solid solution hardening model based on uniform LLD and spherical stress tensor assumption to this kind of solid solutions. This work also questions the traditional view that elementary substitutional solute atoms in metal solid solutions should not induce anelastic relaxation and internal friction.