A graphene-based tunable ultra-narrowband mid-infrared TE-polarization absorber is proposed. The simulation results show that, the absorption peak can be tuned from 5.43896µm to 5.41418µm, by tuning the Fermi level of graphene from 0.2eV to 1.0eV. The simulation results also show that the absorption bandwidth is less than 1.0nm and the absorption rate is more than 0.99 for TE-polarization (electric field is parallel to grating grooves) in the tuning wavelength range. The ultra-narrowband absorption mechanism is originated from the low power loss in the guided-mode resonance. The tuning function is mainly attributed to the change of the real part of the graphene's permittivity. This tunable ultra-narrowband mid-infrared absorber has potential applications in the tunable filtering and tunable coherent emission of thermal source.