  The topological phases in one-dimensional quantum walk can be classified by
the coin parameters. By solving for the general exact solutions of bound states
in one-dimensional quantum walk with boundaries specified by different coin
parameters, we show that these bound states are Majorana modes with
quasi-energy $E=0,\pi$. These modes are qualitatively different for different
boundary conditions used. For two-boundary system with symmetric boundary
conditions, the interaction energy between two Majorana bound states can be
computed, as in the case of a finite wire. Suggestion of observing these modes
are provided.
