A flexible rebound-type acoustic metamaterial with high sound transmission loss (STL) at low frequency is proposed, which is composed of a flexible, light-weight membrane material and a sheet material - Ethylene Vinyl Acetate Copolymer (EVA) with uneven distributed circular holes. STL was analyzed by using both computer aided engineering (CAE) calculations and experimental verifications, which depict good results in the consistency between each other. 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 STL peak is studied by changing the structure parameters and material parameters of the metamaterial, providing a method to design the metamaterial with high sound insulation in a specified frequency range. A group of combined metamaterial is proposed which consist of the metamaterial and felt or PU material, which can avoid some of the resonance frequency points and fill the STL valleys of the pure metamaterial structure. It could achieve 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.