In this paper, the Meshless Local Petrov-Galerkin (MLPG) method is used to analyze the fracture of an isotropic FGM plate. The stress intensity factor of Mode I and Mode II are determined under the influence of various non-homogeneity ratios, crack length and material gradation angle. 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 stress intensity factors (NDSIF) are calculated using the path independent integral, J*, which is formulated for the non-homogeneous material. The Edge-Cracked FGM plate is considered here and analyzed under the uniform load and uniform fixed grip conditions. To validate results, at first, homogeneous and FGM plate with material gradation along crack length was analyzed and compared with exact solution. Results showed good agreement between MLPG and exact solution.