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 the equation of state of neutron star matter and in gravitational theories. In this paper, we have successfully found 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⊙ are strongly correlated with the neutron skin thickness of Pb208 independently of the equation of state, while this correlation depends on the coupling constant in EiBI. As a result, via the direct observations of the radius of the neutron star with 0.5M⊙ and the measurements of a neutron skin thickness of Pb208 by the terrestrial experiments, one could not only discriminate EiBI from general relativity but also estimate the coupling constant in EiBI.