A terahertz graphene tunable absorber consisting of monolayer graphene on a dielectric grating and a substrate separated by a waveguide layer is designed and investigated. The absorber exhibits polarization-independent absorption enhancement at resonance for fully conical light incidence, which is attributed to the simultaneous excitation of two identical guided modes in the waveguide layer. Moreover, the absorber possesses an ultranarrow absorption profile with an ultrahigh quality factor. To intuitively confirm the potential physical mechanism of such phenomena, the electromagnetic field distributions for both polarized light are described. Finally, the influences of Fermi level and relaxation time on the absorption properties are investigated, which present the flexible tunability of the proposed device. It is believed that the conclusions will enable the development of optoelectronic devices by simply combining graphene with a guided-mode resonance structure.