Metamaterial absorber (MA) is a hot research topic recently. To our best knowledge, it is difficult to achieve dual-wavelength high absorption and narrow bandwidth in the near-infrared band at the same time. In this paper, we propose a dual-channel narrow bandwidth MA with a simple structure, which is composed of three layers: a silica substrate, an Au thin layer, and an asymmetric periodic metal grating. Finite-difference time-domain simulations show that the proposed MA has high absorption efficiency at wavelengths λ₁=1.1005 μm and λ₂=1.19024 μm, and the full width at half maximum (FWHM) is only 0.21 nm and 3 nm, respectively. After analyzing the magnetic field distributions of MA, we find that the narrow bandwidth and high absorption at λ₁ are mainly attributed to surface plasmon polariton (SPP) resonance; at λ₂, both SPP resonance and Fabry-Pérot (FP) resonance take effect. Finally, the influence of structural parameters of the MA on its absorption characteristics is assessed, and it is found that the change in MA parameters can achieve the tuning of λ₁ and λ₂.