Abstract: Fit By Order (FBO) method is developed to establish the meshless approximation function at a node, in which the approximation function is first fitted by the linear basis, and then fitted by the quadric basis to minimize the error. Collocation is used to discretize the governing equation. The proposed method has several advantages. Compared with other interpolation methods, such as MLS and PIM, FBO overcomes the difficulties arising from the singularity of matrix and only six nodes are required to establish the approximation, so that the computational effort required is reduced. Compared with Galerkin-based meshless method, the proposed method does not require any mesh, so that the computational cost is further reduced.