Plasmonic nanostructures have attracted remarkable attention in label-free biosensing detection due to their unprecedented potential of high-sensitivity, miniaturization, multi-parameter, and high throughput screening. In this paper, we propose a plasmonic metamaterial absorber consisting of an asymmetrical step-shaped slit-groove array layer and an opaque gold film, separated by a silica dielectric layer, which demonstrates three-resonant perfect absorption peaks at near-infrared frequencies in an air environment.This is equivalent to three reflection dips due to the opaque gold membrane underneath the structure. Originating from the coupling and hybridization of different plasmonic modes, these three absorption peaks show different linewidths and distinctive excellent sensing performance. The surface lattice resonance (SLR) at the short wavelength range enables an ultra-narrow absorption peak of merely 2 nm and a high bulk refractive index sensitivity of 1605 nm/RIU, but occurring with comparatively low surface sensitivity. Compared to the above-mentioned narrowband SLR mode, the other two absorption peaks, respectively stemming from the coupling between slit-cavity mode and the plasmon resonance of different orders, possess relatively broad linewidths and low bulk refractive index sensitivities, yet outstanding surface sensitivities. The complementary sensing performance among these absorption peaks presents opportunities for using the designed plasmonic metamaterial absorber for multi-parameter detection and various complex application scenarios.