Aiming at the insulation of low-frequency acoustic sound, a 100 mm crescent disc asymmetric membrane-type acoustic metamaterial structure was designed in this paper, which was composed of aluminum material as the frame and iron material as the mass attached to the surface of flexible ethylene-vinyl acetate copolymer film. The finite element method was adopted to calculate its transmission loss and displacement field. The asymmetric structure, the structure parameters and the mass block′s eccentricity together with the vibrational modes analysis were investigated in this study for a better sound insulation performance. The results show that, compared with the symmetric membrane-type acoustic metamaterials, the design of the asymmetry in a single cell makes the low-frequency sound insulation band widened by 23 Hz. Meanwhile, more vibrational modes are generated which illustrates that the coexistence of Lorentz resonance and Fano resonance promotes a better sound insulation performance of the crescent disc asymmetric structure. The large-size asymmetric membrane-type acoustic metamaterial structure designed in this paper can reduce the sound insulation frequency to 10 Hz with a wide low-frequency sound insulation performance within 10~500 Hz. It provides a new method for improving the low-frequency sound insulation effect of sound barriers in terms of structural optimization design.