The Fibonacci piezoelectric superlattices (FPSs) with an exteal dc electric field is presented,in which the dc electric field can tune the bandwidth of polaritonic band gaps (PBGs) continuously and reversibly via the electrooptic effect.The absolute bandwidths of two major PBGs of the FPSs around ω =7.5 GHz and ω =12.5 GHz can be broadened from 0.022 GHz to 0.74 GHz and from 0.02 GHz to 0.82 GHz with the dc electric field increasing from 0 to 1.342 × 106 V/m,respectively.The corresponding relative bandwidths of the two major PBGs are widened from 0.28％ to 9.2％ and from 0.18％ to 6.35％,respectively.The general mechanism for the bandwidth tunability is that the coupling strength between the lattice vibration and electromagnetic waves is capable of being altered by the dc electric field via the electro-optic effect.Thus the properties can be applied to construct microwave switchings or field tunable bulk acoustic filters.