We present numerically a dual-band dielectric metamaterial absorber where a silica film layer is inserted between the top asymmetric silicon dimer array and the bottom metal substrate. The simulation results show that we can get two resonance peaks (labeled A and B) with near-perfect absorption in the near-infrared regime. Peak A, which is originated from the cavity resonance in the gaps of the dimers, has a full width at half-maximum (FWHM) of 4.8 nm and quality factor of 407. And peak B, which is originated from the destructive interfering of the asymmetric dimers, has an ultra-narrow bandwidth of 0.0014 nm and quality factor of 1.38×106which are much superior to those of the existing metamaterial absorbers. In addition, the simulations also show that the absorption bandwidths can be further narrowed by adjusting the silica layer thickness. Due to the ultra-narrow bandwidths, peaks A and B have the high figure of merits (FOMs) of 51.4 and 6.0×104. Such high FOMs indicate that the proposed dual-band absorber can be applied as a high-performance refractive index sensor.