In this talk, we will present a set of explicit generators for finite W-superalgebra U(g,e) associated with a basic classical Lie superalgebra g and a minimal even nilpotent element e, and also the commutators between them. In virtue of these, we will introduce the Verma modules for U(g,e), and give a classification of the corresponding irreducible modules. Those Verma modules can be further described via parabolic induction from Whittaker modules for osp(1|2) or sl(2) respectively, depending on the parity of the dimension for a particular subspace of g. We will also introduce an analogue of the BGG category O for U(g,e). This is a joint work with Bin Shu.

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