  We study the edge states for a quantum anomalous Hall system (QAHS) coupled
with a spin-singlet s-wave superconductor through the proximity effect, and
clarify the topological nature of them. When we consider a superconducting pair
potential induced in the QAHS, there appear topological phases with nonzero
Chern numbers, $i.e.$, ${\cal N}=1$ and ${\cal N}=2$, where Andreev bound
states appear as chiral Majorana edge modes. We calculate the energy spectrum
of the edge modes and the resulting local density of states. It is found that
the degenerate chiral Majorana edge modes for ${\cal N}=2$ are lifted off by
applying Zeeman magnetic field along the parallel to the interface or the shift
of the chemical potential by doping. The degeneracy of the chiral Majorana edge
modes and its lifting are explained by two different winding numbers defined at
the time-reversal invariant point of the edge momentum.
