We present the experimental realization and theoretical understanding of a membrane-type acoustic metamaterial with very simple construct, capable of breaking the mass density law of sound attenuation in the 100-1000 Hz regime by a significant margin ( approximately 200 times). Owing to the membrane's weak elastic moduli, there can be low-frequency oscillation patterns even in a small elastic film with fixed boundaries defined by a rigid grid. The vibrational eigenfrequencies can be tuned by placing a small mass at the center of the membrane sample. Near-total reflection is achieved at a frequency between two eigenmodes where the in-plane average of normal displacement is zero. By using finite element simulations, negative dynamic mass is explicitly demonstrated at frequencies around the total reflection frequency. Excellent agreement between theory and experiment is obtained.