We amplified acoustic evanescent waves using metamaterial slabs with a negative effective density. For the amplifying effect of the slab to overcome the dissipation, it is necessary that the imaginary part of the effective density is much smaller than the real part, a condition not satisfied so far. We report the construction of membrane-based two-dimensional negative-density metamaterials which exhibited remarkably small dissipation. Using a slab of this metamaterial we realized a 17-fold net amplitude gain at a remote distance from the evanescent wave source. Potential applications include acoustic superlensing.