To overcome certain limitations like shape control and high acoustic impedance of monolithic piezoelectric materials, piezoelectric fiber-reinforced composites (PFRCs) and piezoelectric-viscoelastic (PV) composites have emerged as obvious and amazing replacements. Particularly in PFRCs, piezoelectric fibers are surrounded by non-piezoelectric materials, and the effective material properties of PFRCs are dependent on both the constituent materials and the amount of piezoelectric fibers (fiber volume fraction) present in the elementary units of the composite. The present research article focuses on the transference of Love-type surface acoustic waves in a PFRC layer sandwiched between a viscoelastic polymer layer and a functionally graded piezoelectric-viscoelastic (FGPV) substrate. The effective material properties of the PFRC layer obtained by the rule of mixtures along with the strength of materials approach are used for mathematical computation. The interface between PFRC and FGPV substrate is mechanically and dielectrically imperfect. The material properties of the FGPV substrate vary along the structure's depth. Dispersion relations have been obtained for both electroded and non-electroded states. Parametric responses of fiber volume fraction, mechanical and electrical imperfections, viscosity, and functional grading on dispersion traits of Love-type wave are demonstrated through graphical plotting. The outcomes of the study can be utilized to theoretically understand the dispersion in PFRCs.