A dual-band terahertz metamaterial absorber composed of two identical square metallic patches and an insulating medium layer on top of a continuous metallic ground is demonstrated. Two resonance peaks (labeled A and B) with near 100% absorbance are obtained, of which peak A derived from the localized resonance of the two square patches has a line-width of 0.2571 THz and quality factor of 6.9156, while peak B which resulted from the hybrid coupling of the localized resonance of the two square patches and surface lattice resonance of the device has a very narrow line-width of 0.0083 THz and large quality factor of 296.2771. Narrow line-width and large quality factor have important prospects in sensing application. Based on this, the sensing performance of the device is explored; it is revealed that peak B exhibits highly sensitive sensing ability (including a sensing sensitivity of 1.9010 THz per RIU and figure of merit of 229.04) in terms of the surrounding index. In addition, the influence of structural parameters on the absorption performance is discussed to further verify the formation mechanism of these two absorption peaks.