<p>In this paper, the fracture mechanics of one-dimensional hexagonal quasicrystals (1D-HQCs) with arbitrary location periodic mode-III cracks emanating from a nanoscale hole is investigated theoretically. According to the Gurtin–Murdoch surface elasticity theory, the surface effects of nano-defects (holes and cracks) are considered. A new deformation mapping function was obtained by using the conformal transformation technology. Combined with the analytical function boundary value problem theory, the generalized stress field of the problem is obtained, and the analytical expressions of the stress intensity factors of the phonon field and the phason field of the arbitrary location crack tip are derived. The effects of crack position angle, crack number, crack length/aperture ratio, phonon field–phason field coupling coefficient and applied loads on the dimensionless stress intensity factors are discussed. The crack position angle significantly affects the generalized stress intensity factors, both with and without surface effects. The stress intensity factors have obvious size effects under considering surface effect. The influence of other factors on the generalized stress intensity factors is different.</p>