The moving crack problem in an infinite plate of orthotropic anisotropy functionally graded materials (FGMs) subjected to an anti-plane shear loading is studied by making use of non- local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form. Fourier transform is employed to solve the partial differential equation. The mixed boundary value problem is reduced to a pair dual integral equations which is solved by using Schmidt’s method. The semi-analytic solution of crack-tip stress is obtained, contrary to the classical elasticity solution, the crack-tip stress fields does not retains the stress singularity. The influences of the characteristic length, graded parameter, orthotropic coefficient and crack velocity on the crack-tip stress are analyzed. The numerical results show that the stress at the crack tip decrease as the characteristic length, crack velocity, graded parameter are increased and increase as the orthotropic coefficient is increased.