The numerical procedure for the evaluation of the one-loop self-energy correction to the g factor of an electron in the 1s and 2s states in H-like ions to all orders in Zα was discussed. It was found that in the Feynman gauge, the calculation was carried out. The Heaviside charge units and the relativistic units were used for the purpose. The results show that the lowest-order value for the g factor was found by a simple relativistic calculation, which was based on the Dirac equation.