Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope whose extreme points are the n × n permutation matrices. Let Ωsn, Ωhsn and Ωπn,denote the sets of symmetric doubly stochastic matrices, Hankel symmetric doubly stochastic matrices and centrosymmetric doubly stochastic matrices respectively. It is clear that Ωsn , Ωhsn and Ωπn are sub-polytopes of Ωn : The extreme points of Ωsn and Ωhsn were discovered, while the extreme points of Ωπn were not characterized completely. We determine all the extreme points and give characterizations of the permutation matrices which generated the extreme points.