It is discussed that the computation of Lefschetz numbers of maps on flag manifolds of compact simple lie G by using Leray-Hirsch property. Some applications in geometry and algebra are given. 利用LerayHirsch性质,对于紧单李群G的旗流形,讨论了其上映射的Lefshetz数的计算,并给出了一些几何和代数中的应用。