Abstract: An accurate velocity filed is important for simulating Darcy flow, solution transport and contaminant migration in heterogeneous porous media. Generally, the velocity results calculated by the conventional numerical methods have low precision and poor continuity. To overcome this defect, two improved weight functions are used to construct the global approximation on manifold elements and two improved NMM codes are developed to eliminate the linear dependence problems caused by the higher-order overburden functions, and the velocity/gradient solutions of node continuity and global continuity are obtained, respectively. Furthermore, the convergence and accuracy of the improved weight function NMM codes are analyzed through several examples.