The dependence between neutron skin thickness and neutron abrasion cross section (ónabr) for neutron-rich nuclei is investigated within the framework of the statistical abrasion ablation model. Assuming that the density distributions for proton and neutron are of Fermi-type, and adjusting the diffuseness parameter of neutron density distribution in the droplet model, we find out the good linear correlation between the neutron skin thickness and the abrasion cross section ónabr for neutron-rich nuclei. The uncertainty of neutron skin thickness determined from ónabr is very small. It is suggested that ónabr can be used as a new experimental observable to extract the neutron skin thickness for neutronrich nucleus. The scaling behaviours between neutron skin thickness and tabr, separately, for isotopes of 26-35Na,44-56Ar, 48-60Ca, 67-7SNi are also investigated.