The Dynamic response analysis of an interface crack between dissimilar functionally graded orthotropic material(FGOM) strips under Mode III impact loading is conducted using integral transform approaches. Mass density and shear moduli of the FGOM strips change continuously along the strip thickness, and weak-discontinuous interface condition is adopted. Laplace and Fourier transforms are applied to reduce the problem to a dual integral equation, which are then converted into the Fredholm integral equations of the second kind. Followings are beneficial to impede dynamic fracture of interface crack of FGOM strips: a) increase of shear moduli from the interface to the upper or lower free surface; b) increase of the gradient of shear moduli in case of increase of shear moduli from the interface to the free surface; c) decrease of the ratio of shear moduli for the Case I and increase of the ratio of shear moduli for the Case II and Case III; d) increase of thickness of the strips.