Graphene’s conductivity is governed by intraband contributions in microwave to terahertz band. The dependence of the surface conductivity, the equivalent surface impedance and permittivity on the chemical potential and temperature using the intraband conductivity model are studied. The surface conductivity and equivalent surface impedance largely depend on the chemical potential, and hardly depend on the temperature. So the graphene has tunable surface conductivity and impedance. The effective surface plasmon polaritons mode index of the infinite planar graphene based on the intraband conductivity model and the dispersion relation of TM (transverse magnetic) modes of graphene’s SPP (surface plasmon polaritons) are researched. The result proves that graphene-based plasmonic resonant antennas are expected to be smaller than traditional material antennas. So the graphene antennas are tunable, stable and miniature. The dependence of transmission coefficient on chemical potential based on the property of electromagnetic waves is studied. The transmission coefficient largely depends on the chemical potential so as to make the material possible for tunable THz filter. Flexible graphene antenna is designed. The good gain is observed.