  We investigate the topological phase transition with large Chern number in a
coupled layer system. The topological transitions between different topological
superfluids can be realized by controlling the binding energy, interlay
tunneling and layer asymmetry {\it etc}. These topological phase transitions
can be characterized by energy gap closing and reopening at the critical points
at zero momentum, where the Pfaffian and Chern number undergo a discontinuous
change. The bulk-edge correspondence ensures that the number of edge modes
exactly equals the Chern number. However all these edge modes localized at the
same edge have the same chirality and propagate along the same direction. These
topological phases can be detected by spin texture at or near zero momentum,
which changes discontinuously across the phase transition point due to band
inversion. This model can be easily generalized to multilayer system in which
the Chern number equals any positive integer --- similar to that in integer
quantum Hall effect --- can be realized. This work paves a new way in the
realization of topological superfluids with large Chern number.
