The modification such as introducing charge is an effective means to make the graphene applicable in the field of electronic devices. In this paper, the first-principle calculation was performed to investigate the electronic and phononic band structures as well as the electron-phonon interaction in a monolayer graphene doped by small number of electrons or holes. It was found that, the charged graphene exhibits metallic character due to the shift of Fermi level. The introducing charge did not affect the variation of bending in graphene since the z-axis acoustic mode was unchanged. The abnormal softened phonon mode was observed for electron-doped graphene. The electron-phonon coupling was constantly enhanced with the increasing of charge concentration. It was concluded that, the carrier mobility in graphene can be improved since the doping adjusts the longitudinal optical phonon frequency and results in a stronger electron-phonon interaction.