Aiming at noise isolation in low frequency range, this paper presents a novel kind of membrane sound insulator featuring a bistable actuation, by combining magnets and multilayer dielectric elastomer actuator (DEA). With a critical applied voltage on DEA, it deforms and the magnets attract in terms of a bistable snapping, which leads to an abrupt stiffness shift, and consequently regulates the sound transmission loss (STL) peak frequency. An electromechanical model is established to reveal the bistable characteristics and to study the effect of voltage and structure parameters for design optimization. The sound-insulation measurement experiment verifies the tunable acoustic performance. The sound-insulation peak frequency has a maximum shift of 142Hz, 130Hz, and 141Hz under voltages of 2000V, 2500V, and 3000V, respectively, showing an advancing figure of merit compared with the existed acoustic metamaterial based on dielectric elastomer.