Membrane-type metamaterial equipped with piezoelectric material membrane is capable of achieving tunable bandgap properties. The accurate prediction of the dispersion relation is paramount for the design and its application. Thus in this study, an analytical model is proposed to calculate the dispersion relation of piezoelectric membrane-type metamaterial. The model is based on the Plane Wave Expansion (PWE) method incorporated with the piezoelectric constitutive equations. It enables the bandgap prediction of this type of metamaterial by adjusting the external voltage applied to the piezoelectric membrane. The effect of the external voltage on the bandgap location tuning is investigated, allowing the bandgap location to be shifted accordingly for disturbance rejection of varying spectral components. Finite element analysis is conducted to examine the accuracy of the proposed analytical model. The results are found to be consistent with each other and they demonstrate that the model can effectively predict the bandgap properties of the piezoelectric membrane-type metamaterial.