A theoretical and numerical study has been conducted to investigate the dynamic crack propagation in functionally graded materials (FGMs) by making use of non-local theory. The variation of the shear modulus and mass density of the FGMs are modeled by a exponential increase along the direction perpendicular to the crack surface. The Poisson’s ratio is assumed to be constant. The mixed boundary value problem is reduced to a pair dual integral equations through Fourier. In solving the dual integral equations, the crack surface displacement is expanded in a series using Jacobi’s polynomials and Schmidt’s method is used. Contrary to the classical elasticity solution, the crack-tip stress fields does not retains the inverse square root singularity. The analysis revals that the peak values of crack-tip stress increase with the the crack velocity as characteristic length is decreased.