A tunable planar auxetic metamaterial for controlling and filtering acoustic waves was investigated. In the study, the commercial finite element software package was utilized for numerical simulations. A planar auxetic structure was placed periodically, and its acoustic band structure was obtained. It was found that the bandages may appear in certain frequency range because of the geometric deformation of the auxetic structure. In addition, the wave attenuation behavior at a specific frequency was investigated experimentally, and the experimental results were compared with those obtained from numerical simulations. Both the numerical and experimental results showed that the planar auxetic structure is tunable for controlling the sound wave propagation and filtering the waves within a specific frequency range.