Highly efficient absorption of light at telecommunication wavelengths in monolayer graphene is numerically and theoretically investigated in a multi-layer photonic configuration, which consists of an ultrathin metal film coated on a dielectric Bragg mirror and a graphene sheet in a silica spacer. Our results show that the absolute absorption of light in the single-atomic-layer graphene can significantly reach 80% (34.8-fold enhancement compared to the intrinsic value of 2.3%), due to the strong field confinement of Tamm plasmon polaritons in the silica spacer. Moreover, we find that the absorption efficiency of graphene is critically dependent on the position of the graphene in the spacer. The operating wavelength is flexibly tunable by adjusting the incident angle of light and the thicknesses of metal and Bragg mirror layers. The meaningful improvement and tunability of graphene absorption may find favorable applications for the realization of high-performance graphene optoelectronic devices, such as detectors and modulators.