Photon from neutron-proton bremsstrahlung in p+Pb reactions is examined as a potential probe of the neutron-skin thickness in different centralities and at different proton incident energies. It is shown that the best choice of reaction environment is about 140MeV for the incident proton and the 95\%-100\% centrality for the reaction system since the incident proton mainly interacts with neutrons inside the skin of the target and thus leads to different photon production to maximal extent. Moreover, considering two main uncertainties from both photon production probability and nucleon-nucleon cross section in the reaction, I propose to use the ratio of photon production from two reactions to measure the neutron-skin thickness because of its cancellation effects on these uncertainties simultaneously, but the preserved about 13\%-15\% sensitivities on the varied neutron-skin thickness from 0.1 to 0.3fm within the current experimental uncertainty range of the neutron-skin size in $^{208}$Pb.