The eigen-frequencies of the axial w-modes of oscillating neutron stars are studied using the continued fraction method with an Equation of State (EOS) partially constrained by the recent terrestrial nuclear laboratory data.It is shown that the density dependence of the nuclear symmetry energy Esym affects significantly both the frequencies and the damping times of these modes.Besides confirming the previously found universal behaviour of the mass-scaled eigen-frequencies as functions of the compactness of neutron stars, we explored several alternative universal scaling functions.Moreover, the wll-mode is found to exist only for neutron stars having a compactness of M/R larger than about 0.1078 independent of the EOS used.