The multi-channel enhanced absorption properties in graphene monolayer are theoretically studied. It is realized by inserting a graphene monolayer in a dielectric film, which is sandwiched between a metallic film and a Fibonacci quasiperiodic structure. It is shown that three peaks with absorbance above 75% can be achieved, which is attributed to the Tamm plasmon polaritons and multiple photonic stopbands of the Fibonacci dielectric multilayers. Moreover, the distribution of the normalized electric field intensity is simulated to reveal the physical origin of such multichannel absorption effect. The designed graphene absorber possesses ultra-narrow absorption profiles and performs similar to an antenna. Furthermore, the multichannel absorption performances could be flexibly tuned by changing the angle of the incident and the geometric dimensions. Our results may find potential applications in the design of novel photoelectronic devices.