The anti-analog giant dipole resonance (AGDR) was separated from other excitations such as the spin-dipole resonance by multipole decomposition analysis of the 208Pb(→p,→n) reaction at a bombarding energy of Tp = 296MeV. The polarization transfer observables were found to be useful for carrying out this separation. The energy difference between the AGDR and the isobaric analog state (IAS)was determined to beΔE = 8.69 ± 0.36MeV,where the uncertainty includes both statistical and systematic contributions. Theoretical calculations using the proton-neutron relativistic quasi-particle random phase approximation predicted a strong correlation between ΔE and the neutron skin thickness ΔRpn. Under the assumption that the correlation predicted in this model is correct, the present ΔE value corresponds to a neutron skin thickness of ΔRpn = 0.216 ± 0.046 ± 0.015 fm, where the first and second uncertainties are the experimental and theoretical uncertainties, respectively.