Two-dimensional (2D) black phosphorus (BP) with direct band gap, bridges the characteristics of graphene with a zero or near-zero band gap and transition metal dichalcogenides with a wide band gap. In the infrared (IR) regime, 2D BP materials can attenuate electromagnetic energy due to losses derived from its surface conductivity. This paper proposes an IR absorber based on 2D BP metamaterials. It consists of multi-layer BP-based nano-ribbon pairs, each formed by two orthogonally stacked nano-ribbons. The multi-layer BP metamaterials and bottom gold mirror together form a Fabry-Perot resonator that could completely inhibit light transmission to create strong absorption through the BP metamaterials. Unlike previously reported BP metamaterial absorbers, this new structure can operate at two frequency bands with absorption > 90% in each owning to the first-order and second-order Fabry-Perot resonant frequencies. It is also polarization independent due to the fourfold rotational structural symmetry. To our best knowledge, this is the first report on using BP metamaterials in an absorber that operates independent of polarization and in dual bands.