Charge-changing cross sections \({\sigma _{cc}}\) for mirror nuclei pair, \(^{22}\) Ne and \(^{22}\) Mg, on carbon and proton targets were measured at 120 MeV/nucleon. The experimental \({\sigma _{cc}^{exp.}}\) were compared with Glauber-type calculations using the known density distribution of the target and the proton distribution of the projectile. Moreover, assuming the perfect charge symmetry, the proton distribution radius of \(^{22}\) Mg was deduced and compared with that from the isotope shift. We examined the possibility of the charge-changing cross section for mirror nuclei as a new method to determine the neutron skin thickness.