Based on the Gurtin-Murdoch surface / interface theory and the complex potential theory, the problem of an electrically semi-permeable nano-sharp crack in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) is analyzed. By constructing conformal mapping of sharp crack, the analytic solutions of the electroelastic field are determined. Meanwhile, the field intensity factors and the energy release rate (ERR) under the electric boundary conditions of semi-permeable are obtained. The effects of length of nano-sharp crack, dielectric constant, the electric loading, the mechanic loadings on the dimensionless stress intensity factors (SIFs), dimensionless electric displacement intensity factor (EDIF) and the dimensionless ERR are considered. The results show that the dimensionless SIFs, EDIF and the ERR have an obvious size dependent effect. The impact of surface effect becomes weaker along with the growth of crack size. The change of the dielectric coefficient has little influence on the dimensionless SIFs, but has a strong influence on the dimensionless EDIF. The obtained analytical solutions are helpful to promote the development of nano quasicrystal (QC) composite mechanics, and provide an important theoretical support for the design and preparation of nano QC materials.