The effect of weak-discontinuous interface on the periodic inner cracks in a laminated functionally graded composite is analyzed under anti-plane shear loads. Fourier transformation and dislocation density functions are employed to reduce the solution of the mixed-boundary value prob- lem for Hilbert- The effects of the type singular integral equation, which are solved by I,obatto-Chebyshevtechnique. FGM nonhomogeneity, the layers thickness, the distance between of cracks and the weak-diccnntinunua interface_ crack snacine on the fracture parameter are discussed in detail.