In this paper, the meshless local Petrov-Galerkin (MLPG) method is used to analyze the Dynamic fracture of an isotropic FGM plate containing a center crack. The Dynamic stress intensity factors are studied under the influence of various non-homogeneity ratios. Both the moving least square (MLS) and the direct method have been applied to estimate the shape function and to impose the essential boundary conditions. The enriched weight function method is used to simulate the displacement and stress field around the crack tip. Normalized Dynamic stress intensity factors (NDSIF) are calculated using the path independent integral, J*, which is formulated for the nonhomogeneous material.To validate the method, the homogenous center cracked plate problem is analyzed. The obtained results show good agreement between the analytical solution and the MLPG results for homogenous material. After validation, a center cracked plate made of FGM with two different material gradations (along and normal to the crack length) and three different lengths of FGM zone under the effect of step load are considered, and the following six distinct problems are studied here.