A polarization-insensitive and double-face-absorbing metamaterial absorber is presented, which is based on chiral structure. The unit cell of this absorber is comprised of a chiral structure and a dielectric substrate. Simulated absorbances under frontal and reverse incident directions indicate that the structure of this absorber is reciprocal, and thus this absorber has double-face-absorption property. Simulated absorbances under different polarization angles indicate that this absorber is polarization-insensitive. Simulated absorbances under different angles of incidence indicate that this absorber is narrow-angled. Simulated surface currents and magnetic energy density of the unit cell indicate that there exists cross coupling between electric field and magnetic field, and that the absorption is related to chirality. Simulated absorbances under different loss conditions indicate that dielectric loss of the substrate is dominant in the absorbing process, and that metal loss can be neglected. This absorber may have potential applications in some double-face-absorbing fields.