A flexible membrane-type acoustic metamaterial, is proposed, with improved sound transmission loss (STL) performance at low frequency. It is composed of a flexible, light-weight membrane material and a sheet material - Ethylene Vinyl Acetate Copolymer (EVA) with an arrangement of periodic holes. The STL was analyzed by using both computer aided engineering (CAE) calculations and experimental verifications, which depict good results in the consistency between both. An obvious sound insulation peak exists in the low frequency band, and the STL peak mechanism is the rebound-effect of the membrane surface, which is proved through finite element analysis (FEA) under single frequency excitation. Then the variation of the peak is studied by changing the structure parameters and material parameters of the metamaterial, providing a method to design sound insulation metamaterials in a specified frequency range. It has achieved light-weight and flexible design in the field of low frequency vibration and noise reduction, which will play a promoting role to realize engineering applications in automotive, aircraft, submarines and other industries.