Abstract: The order relation, as one important relation in the algebra system, is an indispensable tool in algebra study. Several kinds of semigroups, for instance, the regular semigroup, the simple semigroup, the inverse semigroup, together with their respective partial order relations, are introduced. A brief discussion is made of their properties, which produces two conclusions: one is the relation between the periodic simple semigroup and the complete simple semigroup; the other is the relation between the order relation defined in the inverse semigroup and its congruence relation.