A dual-band metamaterial absorber based on local surface plasmon resonance is designed, which is composed of a periodic arrangement of stacked nanodisk structures. The structure unit consists of two dielectric layers and three metal layers. Based on the finite difference time domain method, under the condition of vertically incident plane light, two absorption peaks in the mid-wave infrared and long-wave infrared (MWIR/LWIR) are obtained, and the absorption is greater than 98%. The absorber has good incident state tolerance characteristics. We can modulate the MWIR/LWIR absorption peaks by changing the radius of the stacked disk structure, and MWIR and LWIR dual-band broadband absorption can be achieved by integrating different size elements in the plane. The average absorption is 71% for MWIR with 1.1 µm bandwidth from 3.2 to 4.3 µm and 88% for LWIR with 3 µm bandwidth from 8.5 to 11.5 µm. At the same time, the structure also has effective refractive index (RI) sensitivity characteristics. In the RI range of 1.8-2, the maximum RI sensitivity of the LWIR and the MWIR is 1085 nm/refractive index unit (RIU) and 1472 nm/RIU, respectively.