This article provides a theoretical and numerical treatment of a crack subjected to an anti-plane shear loading in an infinite strip of FGMs. The crack situated in the mid-plane of strip moves at a constant velocity. It is assumed that the shear moduli varies continuously in the thickness direction and is to be of exponential form. The mixed boundary value problem is reduced to a pair dual integral equations by means of nonlocal elasticity theory and integral transform method. The stress field and displacement field for the strip are solved near the tip of the crack by using Schmidt’s method. Then the influences of the characteristic length, graded parameters and crack velocity on the stress at crack tip are studied. Unlike the classical elasticity solution, the magnitude of stress at the crack tip is finite, and it is found that the maximum stress increases with the crack velocity as the strip length is decreased, and the maximum stress decreases with the characteristic length as the graded parameters is increased.