Display omitted •Our theoretical work is innovative, combining anisotropic two-dimensional materials, hyperbolic metamaterials and light field concentration.•Our biaxial hyperbolic metamaterial structure consisting of anisotropic monolayer black phosphorus can achieve topological transition from an elliptical dispersion to a hyperbolic dispersion based on effective medium theory.•Our absorber achieves an average absorption of up to 93.4%, omnidirectionality (up to 70°), and polarization sensitivity from 30 to 90 μm (3.3 to 10 terahertz). It's optimal as far as we know.•Moreover, unlike the physical mechanism of common multilayer metal/dielectric sawtooth absorbers, which is related to slow-light effect, the absorption of our proposed absorber is attributed to the localized surface plasmon resonance, bulk plasmon polaritons and moth-eye effect. We propose a biaxial hyperbolic metamaterials (HMMs) sawtooth absorber using anisotropic black phosphorus (BP) and demonstrate that it can achieve a topological transition from an elliptical dispersion to a hyperbolic dispersion. We also show the material to be an epsilon-near-zero HMM and validate an effective medium theory. Due to BP’s anisotropic permittivity and light confinement, our absorber achieves an average absorption of up to 93.4%, omnidirectionality (up to 70°), and polarization sensitivity from 30 to 90 μm. We gain physical insights about the high absorption using electric field distributions and absorbed power distribution. Unlike the physical mechanism of common multilayer metal/dielectric sawtooth absorbers, which is related to slow-light effect, the absorption of our proposed absorber is attributed to the localized surface plasmon resonance, plasmon polaritons. Our proposed HMM can be applied in the infrared to terahertz region and we conclude by providing practical guidelines for future research on biaxial hyperbolic metamaterials and anisotropic two-dimensional materials.