The anti-plane problems of one-dimensional hexagonal quasicrystals with the central straight cracks in the finite plate are investigated by using the boundary collocation method．The stress functions can be expressed by selecting an appropriate displacement function under the boundary conditions and by using the properties of analytic functions. Then, the related stress intensity factor in the phonon and quantum fields can be obtained from the stress functions．It is shown that only the plate boundary conditions on the half rectangle are needed to be satisfied approximatively when employing the boundary collocation method due to the geometric symmetry. The influence of the stress intensity factor is investigated through numerical examples. The proposed method can be extended to other fracture problems in the one-dimensional hexagonal quasicrystals.