A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gra-dient method and applied to discretizing the Navier-Stokes equation in an unstructured grid. The transform of non-orthogonal diffusion items generated by the scheme in discrete equations is provided. The Delaunay triangulation method is improved to generate the unstructured grid. The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow. The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively. In the former case, a good agreement is achieved in the main velocity and drag coefficient curve. In the latter case, the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment. It is indicated that the factor dif-ference scheme is of higher accuracy, and feasible to be applied to Navier-Stokes equation.