  Motivated by experimental observation of the Kondo-enhanced Andreev transport
[R. S. Deacon \textit{et al.}, PRB \textbf{81}, 121308(R) (2010)] in a hybrid
normal metal-quantum dot-superconductor (N-QD-S) device, we theoretically study
the Kondo effect in such a device and clarify the different roles played by the
normal and superconducting leads. Due to the Andreev reflection in a QD-S
system, a pair of Andreev energy levels form in the superconducting gap, which
is able to carry the magnetic moment if the ground state of the QD is a
magnetic doublet. In this sense, the Andreev energy levels play a role of
effective impurity levels. When the normal lead is coupled to the QD-S system,
on the one hand, the Andreev energy levels broaden to form the so-called
Andreev bound states (ABSs), on the other hand, it can screen the magnetic
moment of the ABSs. By tuning the couplings between the QD and the normal
(superconducting) leads, the ABSs can simulate the Kondo, mixed-valence, and
even empty orbit regimes of the usual single-impurity Anderson model. The above
picture is confirmed by the Green's function calculation of the hybrid N-QD-S
Anderson model and is also able to explain qualitatively experimental phenomena
observed by Deacon \textit{et al.}. These results can further stimulate related
experimental study in the N-QD-S systems.
