A level set method is proposed to simulate the incompressible two-phase flow considering the effect of surface tension. For reinitialization of level set function, a direct approach method is employed, instead of solving hyperbolic type equation. A mixed element is adopted, so that the continuity and Navier-Stokes equations are solved by using the quadratic elements (six-node triangular element and nine-node quadrilateral element), and the level set function is solved by using the linear elements (three-node triangular element and four-node quadrilateral element). In order to verify the accuracy and robustness of the codes, the present methods are applied to a few benchmark problems. It is confirmed that the present results are in good qualitative and quantitative agreements with the existing studies.