The atmospheric window in the infrared (IR) band primarily consists of mid-wave (MWIR, 3-5 μm) and long-wave IR (LWIR, 8-12 μm) bands, also known as the working bands in most of the IR devices. The main factor affecting the device capability includes the absorption efficiency, hence, the absorption material. Herein, a dual-band absorber based on the composite cross structure (CCS) in both MWIR and LWIR bands was proposed, with absorption peaks of 4.28 μm and 8.23 μm. The obtained absorber is with high scalability in the MWIR and LWIR region respectively by tuning the structural parameters. A quadrupole polarization model is proposed for further understanding of the uneven distribution of electromagnetic field that was caused by the change of the center spacing of the embedded structure. Meanwhile, it was shown that the two absorption peaks exhibited good incident angle stability. In addition, as the incident angle of the TM mode increases, a waveguide is formed between the embedded structure and the surface structure, leading to another strong absorption in the LWIR band. The results showed that absorption increases as the incident angle increases. The proposed absorber can be a good candidate for applications in thermal emission, detection and solar energy harvesting.