Abstract: Functionally graded materials (FGMs) are usually modeled, in numerical analysis, by using a graded distribution of material parameters, such as the Young's modulus. This leads to more complicated stress field and poses certain difficulties in numerical simulations. On the other hand, high-order meshfree methods reproduce stress field more accurately. However, they require much more integration points which leads to inefficiency. In this study, the quadratically consistent meshfree method, originally developed for homogeneous materials, was directly applied to FGM. Numerical results show that the number of integration points are dramatically reduced and meanwhile, the high level of accuracy and convergence of high-order meshfree methods are maintained. As a result, the proposed quadratically consistent meshfree method remarkably improves the computational efficiency of meshfree analysis of FGM.