  Effects of the density dependence of the nuclear symmetry energy on
ground-state properties of superheavy nuclei are studied in the relativistic
mean-field theory. It is found that the softening of the symmetry energy plays
an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of
spherical orbitals in superheavy nuclei. The calculation based on the
relativistic mean-field models NL3 and FSUGold supports the double shell
closure in $^{292}120$ with the softening of the symmetry energy. In addition,
the significant effect of the density dependence of the symmetry energy on the
neutron skin thickness in superheavy nuclei are investigated.
