In recent years, researchers utilized Tamm plasmon polaritons (TPPs) in conventional heterostructures composed of a metal layer, a dielectric spacer layer and an all-dielectric one-dimensional (1-D) photonic crystal (PhC) to achieve high-efficiency absorption of graphene. According to the Bragg scattering theory, photonic bandgaps (PBGs) in all-dielectric 1-D PhC strongly shift toward shorter wavelengths (i.e., blueshift) as the incident angle increases. Therefore, TPPs in conventional heterostructures also show strongly blueshift property. Such strongly blueshift property of TPPs greatly limits the operating angle range of the high-efficiency absorption of graphene. Herein, we realize an angle-insensitive TPP in a heterostructure composed of a metal layer, a dielectric spacer layer and a 1-D PhC containing hyperbolic metamaterial layers. Empowered by the angle-insensitive property of the TPP, we achieve wide-angle high-efficiency absorption of graphene. The operating angle range (A > 80%) reaches 41.8 degrees, which is much larger than those in the reported works based on TPPs and defect modes. Our work provides a viable route to designing cloaking devices and photodetectors.