Level Set method including its advantages and disadvantages was first introduced to trace moving interface.Compared with other methods for tracing of moving interface,Level Set method is more flexible,without using complicated reconstruction technique of interface,so it can be easily programmed.Level Set equation was solved by using RKDG(Runge-Kutta Discontinuous Galerkin) finite element method.RKDG method was used to trace the two dimensional constant flow,rotating flow and shear flow,the method proposed was compared with the other methods for tracing of moving interface.The result shows that not only RKDG method can capture the moving interface accurately but also obtained high resolution ratio computational results.