In this letter, a membrane-type acoustic metamaterial with a compact magnet (MAMM) is presented. To investigate its frequency-tunable properties, a theoretical model considering both static and dynamic effects of magnetic force is established. Analytical investigations indicate that tuning of the magnetic force exerted on the centralized rigid iron platelet leads to the shift in the MAMM's transmission loss peaks. The experimental anti-resonance frequencies of the MAMM derived from the impedance tube measurements exhibited good consistency with those predicted theoretically. Continuously tuned in a wide frequency range, this structure can well adapt to the noise source variation in insulation design.