Abstract: A membrane-type absorber usually requires a large back cavity for the low frequency sound absorption.In order to design a compact low frequency membrane-type absorber,magnetic negative stiffness was introduced to reduce the stiffness of the back cavity.With the use of the transfer matrix method,a theoretical model was established by introducing the negative stiffness mechanism to the model.It is demonstrated that a small cavity with the negative stiffness can simulate the acoustic impedance of a large cavity without and shift the absorption peak frequencies downwards.During the experiments,the absorption peaks at different cavities are downwards obviously in a given magnetic field due to the negative stiffness.Analytical results are compared with the experimental data from the impedance tube test.Good agreement validates that the negative stiffness can shift the absorption peak frequencies downwards and implements a compact design for the low frequency membrane-type absorber.