Metamaterial absorbers display potential applications in the field of photonics and have been investigated extensively during the last decade. We propose a dual-band resonant metamaterial absorber with right-angle shaped elements (RAEs) in the terahertz range based on numerical simulations. The absorber remains insensitive to a wide range of incidence angles (0° – 70°) by showing a minimum absorbance of ~80% at 70°. Furthermore, the proposed absorber is highly independent on any state of polarization of the incidence electromagnetic wave due to the high absorbance, i.e., greater than 80%, recorded for the considered polarization states. To further comprehend the slight variations in absorbance as a function of change in the angle of incidence, the impedance of the structure has been critically examined. The metamaterial absorber is simple in design, and we provide a possible path of fabrication.