To describe the interface evolution in multiphase flows, the numerical simulation requires special approaches. The Lagrangian-based methods (front tracking) are not adequate when the interface curvature is sharp and time dependent. The volume of fluid method is numerically prohibitive. The level set method (LSM) presents many advantages, when a very high accuracy in the interface curvature is needed. In this paper, the LSM is treated in more detail. A finite element (FEM) formulation has been used to model a two-phase flows involving interface propagation. A variational formulation is introduced in order to suppress the costly re-initialization procedure, and a new mass conservation correction method based on penalty factor is proposed. The performance of the method is then presented using several reported cases. The results showed that the accuracy of the proposed approach is drastically improved in comparison with other reported methods. The method is applied to the dam-break and to the rising bubble in water column problems. Good agreements with the reported solutions are presented, which corroborates the accuracy of the method.