An extended finite element method based on SUPG/PSPG is proposed to simulate the two phase flow problems. A corrected XFEM is introduced to ensure the blending element to satisfy the Partition of Unity in processing the discontinuity of the interface. Level set method is adopted to track the kinetic phase interface as the fluid flow. Free oscillation is numerically simulated with the presented method. The obtained numerical results are in consistent with the analytical and experimental results. Additionally, breaking dam problem is considered, the numerical solutions agree well with experimental results which illustrate the correctness and efficiency of the proposed method. No re-meshing is needed during the simulation of the two phase fluid flow and the moving interface can be accurately tracked by means of the presented method.