  The finite nuclear-size effect on the leading bound-electron g factor and the
one-loop QED corrections to the bound-electron g factor is investigated for the
ground state of hydrogen-like ions. The calculation is performed to all orders
in the nuclear binding strength parameter Z\alpha\ (where Z is the nuclear
charge and \alpha\ is the fine structure constant) and for the Fermi model of
the nuclear charge distribution. In the result, theoretical predictions for the
isotope shift of the 1s bound-electron g factor are obtained, which can be used
for the determination of the difference of nuclear charge radii from
experimental values of the bound-electron g factors for different isotopes.
