We present a design of a polarization-insensitive dual-band metamaterial absorber (MA) in the THz region by employing a three-layer structure consisting of a rectangular-shaped resonator on top of silicon and metallic film. Finite-difference time domain (FDTD) simulation indicates that two perfect absorption peaks can be achieved at 5.35 and 9.0 THz with absorptivity greater than 96% under normal incidence. The asymmetry in design structure eliminates any polarization dependence, and absorptivity is nearly 80% for large incidence angle up to 60°. The individual absorption band can be tuned by varying the dimensions of the rectangular-shaped resonator. The design idea provides a new strategy to achieve polarization-insensitive MA by arranging structure and can be extended to other bands.