  An alternative way to constrain the density dependence of the symmetry energy
with the slope of the neutron skin thickness of nuclei which shows a linear
relation to both the isospin asymmetry and the nuclear charge with a form of
Z^{2/3} is proposed. The linear dependence of the neutron skin thickness on the
nuclear charge and isospin asymmetry is systematically studied with the data
from antiprotonic atom measurement experimentally and the extended Thomas-Fermi
approach incorporated the Skyrme energy density functional theoretically. An
obviously linear relationship between the slope parameter L of the symmetry
energy and the slope of the neutron skin thickness on the isospin asymmetry can
be found by adopting 66 Skyrme interactions in the calculation. Combining the
available experimental data, the constraint of 16<L<66 MeV on the slope
parameter of the symmetry energy is obtained. The Skyrme interactions
satisfying the constraint are selected.
