Electromagnetic metamaterials (EM) provide novel properties unavailable with natural materials.During the past decade, materials that display analogous behavior in the acoustic realm, so-called acoustic metamaterials, have also attracted much research.Due to their specialized structures, acoustic metamaterials offer many unusual properties and behaviors, such as negative mass density, negative bulk modulus, and negative refractive index ("double-negativity").Although metamaterials that exhibit negative properties have been obtained by trial and error experimentally, our aim is to use topology optimization directly to design negative bulk modulus acoustic metamaterials at particular prescribed frequencies.This paper proposes a topology optimization method for the structural design of an acoustic metamaterial that achieves negative bulk modulus at a certain frequency when the metamaterial is exposed to sound.The presence of grayscales in optimized configurations is difficult to avoid in conventional optimization methods, and is an obstacle to manufacturing, so a level set-based boundary expression is applied here to obtain clear boundaries in the optimized structures.The optimization problem is formulated for a two-dimensional wave propagation problem using the effective medium description, with the objective to minimize the effective bulk modulus at a chosen target frequency, and an S-parameter approach is introduced to derive the effective properties of the acoustic metamaterial.After formulating the optimization problem, the optimization procedure is constructed as follows: the finite element method (FEM) is used to solve the Helmholtz equation for acoustic waves, sensitivities are obtained by the adjoint variable method (AVM), and a reaction-diffusion equation is used to update the level set function.Finally, a numerical example with a prescribed target frequency is provided to illustrate that the proposed method can provide a clear, optimized structure for the design of a negative bulk modulus acoustic metamaterial.