In this paper, a robust local polynomial collocation method is presented. Based on collocation, this method is rather simple and straightforward. The present method is developed in a way that the governing equation is satisfied on boundaries as well as boundary conditions. This requirement makes the present method more accurate and robust than conventional collocation methods, especially in estimating the partial derivatives of the solution near the boundary. Studies about the sensitivity of the shape parameter and the local supporting range in the moving least square approach and the convergence of the nodal resolution are carried out by using some benchmark problems. This method is further verified by applying it to a steady-state convection–diffusion problem. Finally, the present method is applied to calculate the velocity fields of two potential flow problems. More accurate numerical results are obtained.Copyright © 2012 John Wiley & Sons, Ltd.