  Direct observations of neutron stars could tell us an imprint of modified
gravity. However, it is generally difficult to resolve the degeneracy due to
the uncertainties in equation of state (EOS) of neutron star matter and in
gravitational theories. In this paper, we are successful to find the
observational possibility to distinguish Eddington-inspired Born-Infeld gravity
(EiBI) from general relativity. We show that the radii of neutron stars with
$0.5M_{sun}$ are strongly correlated with the neutron skin thickness of
${}^{208}$Pb independently of EOS, while this correlation depends on the
coupling constant in EiBI. As a result, via the direct observations of radius
of neutron star with $0.5M_{sun}$ and the measurements of neutron skin
thickness of ${}^{208}$Pb by the terrestrial experiments, one could not only
discriminate EiBI from general relativity but also estimate the coupling
constant in EiBI.
