Reducing the ducted-fan noise at the low frequency range remains a big technical challenge. This study presents a passive approach to directly suppress the dipole sound radiation from an axial-flow fan housed by a tensioned membrane with cavity backing. The method aims at achieving control of low frequency noise with an appreciable bandwidth. The use of the membrane not only eliminates the aerodynamic loss of flow, but also provides flexibility in controlling the range of the stopband with high insertion loss by varying its tension and mass. A three-dimensional model is presented which allows the performance of the proposed device to be explored analytically. With the proper design, this device can achieve a noise reduction of 5 dB higher than the empty expansion cavity recently proposed by Huang et al. [J. Acoust. Soc. Am. 128, 152-163 (2010)]. Through the detailed modal analysis, even in vacuo modes of the membrane vibration are found to play an important role in the suppression of sound radiation from the dipole source. Experimental validation is conducted with a loudspeaker as the dipole source and good agreement between the predicted and measured insertion loss is achieved.