Piezoelectric acoustic sensor with negative impedance matching circuit is put forward to enhance its sensitivity at low frequencies. The multi-physics problem coupled with sound wave equations, structure stress-strain equations, piezoelectric constitutive equations and electric ordinary equations is analyzed with FEM in detail. Frequency response characteristics are simulated when shunted with negative-capacitance, resistance in series. Sensitivity is obtained from 1kHz to 5kHz. When used proper electrical elements, the sensitivity of the piezoelectric sensor can even exceed that of no matching circuit over 2 factors in broad band.