According to the principle of photoelastic modulated interfermeter, the impedance matching features of piezoelectric crystal has been analyzed and calculated firstly based on the equivalent circuit method,then the ideal matching condition between the piezoelectric crystal and the signal source has been derived,and finally the theoretical relation of inductance and capacitance in the impedance matching network has been obtained.In order to validate the proposed theory, some impedance matching experiments are designed and implemented.The experiment results indicate that the vibration performance of photoelastic modulated interfemeter has been optimized after using the impedance matching network. Meanwhile,the electronic quality factor of the driving controller is raised so that it leads to 40% increase of optical path difference, which improves the spectral resolution of the photoelastic modulated Fourier transform spectrometer.