  In this paper, we consider the D-brane, especially ${\rm D}_-$-brane, in the
pp-wave background, which has the eight dynamical and the eight kinematical
supercharges. Since the pp-wave background has not a SO(8) but a ${\rm SO}(4)
\times {\rm SO}(4)$ symmetric group, the D-brane world-volume theory has a
non-trivial symmetric group which depends on the configuration of D-brane.
Here, we will analyze the open string spectrum consistent with the non-trivial
symmetric group and, at the low energy limit, classify the field contents of
the D-brane world-volume theory which come from the fermionic zero modes of the
open string.
