In this paper, an edge-based smoothed finite element method (ES-FEM) is proposed to solve incompressible fluid flow problems. To stabilize the convection caused oscillation, the characteristic-line method is employed. To stabilize the pressure caused oscillation, the polynomial pressure projection (P3) is used. The proposed stabilization is denoted as CBP3 scheme. One excellent merit of CBP3 scheme is that it suits for all types of elements, even for the simplicial 3-node triangular elements. The CBP3 scheme is implemented into ES-FEM with T3 element, and it is denoted as CBP3/ES-FEM-T3. To verify proposed CBP3 scheme and check its stability, the benchmark problems are used and examined in detail, using both CBP3/ES-FEM-T3 and CBP3/FEM-T3 for comparison. It is found that the CBP3 scheme stabilizes solutions form both FEM and ES-FEM. A convergence study are also carried out, and it reveals that CBP3/ES-FEM-T3 outperforms CBP3/FEM-T3 on accuracies of both velocity and pressure for the tested problems.