The solutions of the Navier-Stokes equation for a Newtonian flow through a 4/1 contraction tube were obtained numerically using the Galerkin finite element method with the nine-node Lagrangian element which was believed to be one of the most accurate tools for mixed-type interpolating formulations. It was proved from this study that the vortex occurrence in the entrance corner region were confirmed but its size was gradually decreased with the increase of Reynolds numbers, and that the velocity profiles and pres-sure distributions along the applied mesh layers were in agreement with the experimental and the previously reported numerical results.