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A tunable dual-band terahertz absorber is designed and investigated. The unit cell of the proposed absorber consists of a graphene monolayer on a guided-mode resonant filter. The graphene absorber presents >40％ absorption at two resonance frequencies, which is attributed to the guided mode resonances with different mode numbers. The electric field intensity distribution is analyzed to disclose the physical mechanism of such a dual-band absorption effect. Furthermore, the influence of optical properties of graphene, including Fermi level and relaxation time, on the absorption spectra are investigated. Finally, the influence of geometric parameters on the absorption spectrum is studied, which will provide useful guidance for the fabrication of this absorber. We believe that the results may be useful for developing the next-generation graphene-based optoelectronic devices.