Hydrogen desorption and its migration on the graphene surface under the alternating electric field have been investigated with the tight-binding molecular dynamics and a large-scale diffusion model. The temperature and field amplitude were set within a range of 1000 to 1500 K and 0 to 1 V/& Aring;, respectively. Field-induced oscillations of hydrogen atom were found to be essentially anharmonic. The optimal amplitude-dependent field frequencies resulting in the highest hydrogen displacement have been defined. The activation energies and frequency factors related to desorption and migration processes at varying electric field amplitudes have been calculated. Based on the microscopic data, we have proposed a diffusion model for hydrogens on locally irradiated graphene applicable at room temperature. A valuable reduction in the concentration of hydrogen in the irradiated graphene was observed. The width of the transition region between the non-irradiated graphene with high hydrogen concentration and the irradiated graphene with a reduced hydrogen concentration has been estimated.