In this paper, we study the states of electron in one-dimensional potential Ｖn＝λｃｏｓ（Ｑn＋ａｎｖ）（０＜ｖ＜１），calculate the eigenvalues and localized exponents. For Ｑ＝２π／３, the energy band is constructed by three subbands. There are two mobility edges in every subband provided that λ<2. We study the nature of the localized and extended eigenstates and mobility edge of this system as a function of λ，ν and α.