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Two essential steps in numerical simulation of a flow field are discretization of the computational space and discretization of the governing partial differential equations (pde’s). In the present work a triangular unstructured grid is utilized. Unstructured grids are recognized to be superior for complex geometries as well as for grid adaptation. For descritization of governing pde’s a finite element method is employed. This research presents a new implicit finite element method in a triangular unstructured grid. For convection term of Navier–Stokes equation a conservative upwind method is used, while a finite element method is used for viscous terms. Results are very promising for viscous flows inside a driven cavity.