Series convergent is a research fields which has the great significance in functional analysis. In order to study the problem of absolutely convergent series, an abstract duality pair (E, F) which has the universal meaning on the basis of literature [4] was introduced, in the pair, F ⊆ G^E, where G is locally convex space. And then the definition of absolutely convergent series on it was given, the relationship between subseries convergent and absolute convergent was discussed, also a Orlicz-Pettis theorem of absolutely convergent series was obtained, that is, the topology of uniform convergence in every M ∈ B_op(E, F) has the same absolutely convergent series. Such a conclusion expands the serviceable range of absolute convergence Orlicz-Pettis Theorem, which is very important to the study of absolute convergence theory, and is an effective way to depict the space to a certain extent.