•A general phase-field fracture model of piezoelectric QCs is proposed.•Influence of electric field on the fracture behaviors of QCs is thoroughly studied.•Anisotropic fracture toughness of piezoelectric QCs is considered.•Various fracture problems of piezoelectric QCs can be studied based on the PFM. In this paper, an electro-elastic phase field model is developed for brittle fracture in piezoelectric quasicrystals. The elastic field of quasicrystals is composite of a phonon field and a phason field. The phonon field, phason field and electric field are coupled with each other, and the phonon and electric loadings trigger the variation of both the phonon and phason elastic energies, which then together contribute to crack evolution. The cracks initiation and propagation in piezoelectric quasicrystals under quasi-static mechanical loading and electric loading can be well predicted. Several numerical examples are performed to evaluate the effects of electric field and anisotropic fracture toughness. Simulation results show that the electric field influences the initial force, peak force, fracture displacement and crack path. For the single-edge notched tensile test, the effects of electric field force on the initial force, peak force and fracture displacement are obvious. For the single-edge notched shear test, the electric field force has no effect on the initial force, but it affects the peak force, fracture displacement and crack path. For the porous plate tensile test, a high-intensity electric field can deflect crack substantially resulting in passing through different holes. Further simulation indicates that the anisotropic fracture toughness has a significant effect on peak force, fracture displacement, and crack path. The present model can be used to simulate various fracture problems of piezoelectric quasicrystals.