Abstract: In this paper, Level Set method is introduced and adoptedto capture moving interfaces of two concentric circles in constantvelocity fields, these of circle and rectangle in shear velocity flowfields, and thoseof hemicycle and Zaleska in revolving velocity flow fields. First LevelSet equation is treated with fifth-order WENO scheme andintegral-averaging scheme, and then it is re-initialized and calculatedagain with modified Godunov method. By analyzing the results, the influenceof discrete accuracy of time derivative and that of re-initialization of Level Set function on tracking effect are studied. It is shown that not only Level Set method can be used to exactlytrack interfaces and get a sharp geography, but also it can be easilyprogrammed.