The difference in the mean-square nuclear charge radius of xenon isotopes was measured utilizing a method based on extreme ultraviolet spectroscopy of highly charged Na-like ions. The isotope shift of the Na-like D1 (3s 2 S 1/2 - 3p 2 P 1/2) transition between the 124Xe and 136Xe isotopes was experimentally determined using the electron-beam ion-trap facility at the National Institute of Standards and Technology. The mass-shift and the field-shift coefficients were calculated with enhanced precision by the relativistic many-body perturbation theory and multiconfiguration Dirac-Hartree-Fock method. The mean-square nuclear charge radius difference was found to be δ〈r 2〉136,124 = 0.269(42) fm2. Our result has smaller uncertainty than previous experimental results and agrees with the literature values.