To solve the multi-objective optimization problem of functionally graded plates with cutouts,a method integrating extended isogeometric analysis（ XIGA） and material distribution variation is proposed. For the mechanical calculation of functionally graded plates with cutouts,the third-order shear deformation theory is introduced,and the extended geometric analysis is adopted. To improve the numerical accuracy,the quadtree adaptive gauss integral is used in the hole boundary region.The B-spline function is used to replace the traditional functional grade material distribution function in the description of material properties. In the optimization process,the control points describing material distribution are taken as design variables to establish multi-objective optimization problems with the largest first natural frequency,the smallest plate mass and the largest buckling critical parameters. The NSGA-II algorithm is selected as the optimization algorithm. The effectiveness of the proposed algorithm is demonstrated by some examples in this paper.