In this talk, we will complete the proof of the classification theorem of irreducible modules over type A principal finite W-suepralgebras by Brown-Brundan-Goodwin [2013]. In particular, all of these modules can be explicitly obtained by tensor product of irreducible modules over gl(1) or gl(1|1). We expect a careful study of this special case will not only provide useful information toward the general nilpotent case but also provide new insights to the study of Whittaker modules over gl(m|n).